Citations

This page contains a list of works cited in the project. You may also be interested in the errata page where we collect errors we have encountered in the literature.

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Works referenced

  • D. D. Anderson and V. Camillo. Armendariz rings and Gaussian rings. Taylor \& Francis (1998)
  • F. W. Anderson and K. R. Fuller. Rings and categories of modules. Springer Science \& Business Media (2012)
  • D. D. Anderson and M. Zafrullah. The Schreier property and Gauss’ lemma. (2007)
  • V. Andrunakievic. Rings without nilpotent elements and completely simple ideals. (1968)
  • E. P. Armendariz and J. K. Park. Compressible matrix rings. Cambridge University Press (1984)
  • G. Baccella. Exchange property and the natural preorder between simple modules over semi-Artinian rings. Elsevier (2002)
  • H. Bass. Finitistic dimension and a homological generalization of semi-primary rings. (1960)
  • V. Bavula. The algebra of one-sided inverses of a polynomial algebra. Elsevier (2010)
  • S. K. Berberian. Baer rings and Baer∗-rings. (1988)
  • S. K. Berberian. The center of a corner of a ring. Elsevier (1981)
  • G. M. Bergman. A ring primitive on the right but not on the left. JSTOR (1964)
  • G. M. Bergman. Coproducts and some universal ring constructions. (1974)
  • G. M. Bergman. Some examples of non-compressible rings. Taylor \& Francis (1984)
  • A. K. Boyle. Hereditary 𝑄𝐼-rings. (1974)
  • W. Brandal. Almost maximal integral domains and finitely generated modules. (1973)
  • W. Brandal. Constructing B\'ezout domains. JSTOR (1976)
  • W. Brandal. On ℎ-local integral domains. (1975)
  • V. P. Camillo. Semihereditary polynomial rings. (1974)
  • V. Camillo and P. P. Nielsen. McCoy rings and zero-divisors. Elsevier (2008)
  • V. P. Camillo and H.-P. Yu. Exchange rings, units and idempotents. Taylor \& Francis (1994)
  • V. Camillo, F. Costa-Cano, and J. Sim\'on. Relating properties of a ring and its ring of row and column finite matrices. Elsevier (2001)
  • V. P. Camillo, D. Khurana, T. Lam, W. Nicholson, and Y. Zhou. Continuous modules are clean. Elsevier (2006)
  • V. Camillo, W. Nicholson, and M. Yousif. Ikeda--Nakayama rings. Elsevier (2000)
  • M. Canfell. Completion of Diagrams by Automorphisms and Bass′ First Stable Range Condition. Elsevier (1995)
  • G. W. Chang. Some Characterizations of {K}rull domains. The Kangwon-Kyungki Mathematical Society (1999)
  • A. W. Chatters and C. R. Hajarnavis. Rings with chain conditions. Pitman Advanced Pub. Program (1980)
  • H. Chen and F. Li. Exchange rings having ideal-stable range one. Springer (2001)
  • P. L. Clark. Commutative Algebra. (2015)
  • J. Clark and P. Smith. On semi-Artinian modules and injectivity conditions. Cambridge University Press (1996)
  • J. Clark, C. Lomp, N. Vanaja, and R. Wisbauer. Lifting modules: supplements and projectivity in module theory. Springer Science \& Business Media (2008)
  • P. M. Cohn. Bezout rings and their subrings. (1968)
  • P. M. Cohn. Free ideal rings. Academic Press (1964)
  • P. M. Cohn. Free ideal rings and localization in general rings. Cambridge University Press (2006)
  • P. M. Cohn. Some remarks on the invariant basis property. Elsevier (1966)
  • J. Commelin and R. Y. Lewis. Formalizing the ring of Witt vectors. (2021)
  • I. G. Connell. On the group ring. Cambridge University Press (1963)
  • J. H. Cozzens. Homological properties of the ring of differential polynomials. (1970)
  • J. H. Cozzens. Simple principal left ideal domains. Elsevier (1972)
  • R. F. Damiano. A right PCI ring is right Noetherian. (1979)
  • W. Dicks. Hereditary group rings. Oxford University Press (1979)
  • W. Dicks and A. Schofield. On semihereditary rings. Taylor \& Francis (1988)
  • A. J. Diesl, C. Y. Hong, N. K. Kim, and P. P. Nielsen. Properties which do not pass to classical rings of quotients. Elsevier (2013)
  • J. Dieudonn\'e and A. Grothendieck. Crit{è}res diff{\'e}rentiels de r{\'e}gularit{\'e} pour les localis{\'e}s des alg{è}bres analytiques. Academic Press (1967)
  • F. Dischinger and W. Müller. Left PF is not right PF. Taylor \& Francis (1986)
  • N. V. Dung and P. F. Smith. On semi-artinian V-modules. Elsevier (1992)
  • D. Eisenbud. Commutative Algebra: with a view toward algebraic geometry. Springer Science \& Business Media (2013)
  • S. Elliger. On simple injective rings. (1973)
  • V. Erdoǧdu. Coprimely packed rings. Elsevier (1988)
  • A. Facchini. On the structure of torch rings. JSTOR (1983)
  • C. C. Faith. Rings and things and a fine array of twentieth century associative algebra. American Mathematical Soc. (2004)
  • C. Faith. Algebra II Ring Theory: Vol. 2: Ring Theory. Springer Science \& Business Media (2012)
  • C. Faith. Lectures on injective modules and quotient rings. Springer (2006)
  • C. Faith. Rings whose modules have maximal submodules. JSTOR (1995)
  • C. Faith. Rings with ascending condition on annihilators. Cambridge University Press (1966)
  • C. Faith. Self-injective rings. (1979)
  • C. Faith. Subrings of self-injective and FPF rings. Springer (1982)
  • C. Faith and P. Menal. A counter example to a conjecture of Johns. (1992)
  • C. Faith and S. Page. FPF Ring Theory: Faithful modules and generators of mod-R. Cambridge University Press (1984)
  • B. Fisher. Notes on Witt vectors: a motivated approach. (1999)
  • E. Formanek and R. L. Snider. Primitive group rings. (1972)
  • R. M. Fossum. The divisor class group of a Krull domain. Springer Science \& Business Media (1973)
  • K. R. Fuller. Artinian Rings: A Supplement to Rings and Categories of Modules. Editum (1989)
  • D. Gill. Almost maximal valuation rings. Wiley Online Library (1971)
  • L. Gillman and M. Jerison. Rings of Continuous Functions. Springer New York (1960)
  • R. W. Gilmer. Integral domains which are almost Dedekind. JSTOR (1964)
  • R. W. Gilmer. Multiplicative ideal theory. M. Dekker (1972)
  • R. W. Gilmer. On prüfer rings. (1972)
  • R. Gilmer and W. Heinzer. Products of commutative rings and zero-dimensionality. (1992)
  • R. Gilmer and T. Parker. Divisibility properties in semigroup rings.. University of Michigan, Department of Mathematics (1974)
  • R. Gilmer and T. Parker. Semigroup rings as Prüfer rings. Duke University Press (1974)
  • R. W. Gilmer and others. On polynomial rings over a Hilbert ring.. The University of Michigan (1971)
  • Github. dart_data github issues. (2024)
  • S. Glaz. Commutative coherent rings. Springer (2006)
  • K. Goodearl. Simple self-injective rings need not be artinian. Taylor \& Francis (1974)
  • K. R. Goodearl. Ring theory: Nonsingular rings and modules. CRC Press (1976)
  • K. R. Goodearl. Von Neumann regular rings. Krieger Pub Co (1991)
  • K. R. Goodearl and R. B. W. Jr. An introduction to noncommutative Noetherian rings. Cambridge University Press (2004)
  • K. Goodearl, P. Menal, and J. Moncasi. Free and residually Artinian regular rings. Academic Press (1993)
  • A. Grams. Atomic rings and the ascending chain condition for principal ideals. (1974)
  • C. Hajarnavis and N. Norton. On dual rings and their modules. Elsevier (1985)
  • J. Han and W. Nicholson. Extensions of clean rings. Taylor \& Francis (2001)
  • D. Handelman. Perspectivity and cancellation in regular rings. Elsevier (1977)
  • W. J. Heinzer and others. Polynomial rings over a Hilbert ring. (1984)
  • M. Henriksen. On the prime ideals of the ring of entire functions.. Pacific Journal of Mathematics (1953)
  • Y. Hirano. On annihilator ideals of a polynomial ring over a noncommutative ring. Elsevier (2002)
  • W. Ho\lubowski, M. Maciaszczyk, and S. \.Zurek. Note on Sus̆kevic̆’s problem on zero divisors. Taylor \& Francis (2017)
  • C. Huh, H. K. Kim, N. K. Kim, and Y. Lee. Basic examples and extensions of symmetric rings. Elsevier (2005)
  • C. Huh, Y. Lee, and A. Smoktunowicz. Armendariz rings and semicommutative rings. Taylor \& Francis (2002)
  • H. C. Hutchins. Examples of commutative rings. Polygonal Pub House (1981)
  • S. U. Hwang, Y. C. Jeon, and Y. Lee. Structure and topological conditions of NI rings. Elsevier (2006)
  • N. A. Immormino. Clean rings \& clean group rings. Bowling Green State University (2013)
  • M. C. Iovanov and A. Sistko. On the Toeplitz-Jacobson algebra and direct finiteness. (2016)
  • N. Jacobson. Basic algebra I. Courier Corporation (2012)
  • N. Jacobson. Basic algebra II. Courier Corporation (2012)
  • N. Jacobson. Structure of rings. American Mathematical Soc. (1956)
  • P. Jaffard. Les syst{è}mes d'id{\'e}aux. Dunod (1960)
  • D. Jonah. Rings with the minimum condition for principal right ideals have the maximum condition for principal left ideals. Springer (1970)
  • I. Kaplansky. Commutative rings. University of Chicago Press Chicago (1974)
  • I. Kaplansky. Dual rings. JSTOR (1948)
  • I. Kaplansky. On the Dimension of Modules and Algebras, X: A Right Hereditary Ring which is not left Hereditary. Cambridge University Press (1958)
  • I. Kaplansky. Rings of operators. Benjamin (1968)
  • I. Kaplansky. Rings with a polynomial identity. (1948)
  • H. J. Keisler. Elementary calculus: An infinitesimal approach. Courier Corporation (2012)
  • J. W. Kerr. An example of a Goldie ring whose matrix ring is not Goldie. Academic Press (1979)
  • D. Khurana and T. Lam. Rings with internal cancellation. Elsevier (2005)
  • A. A. Klein. A simple proof of a theorem on reduced rings. Cambridge University Press (1980)
  • M. T. Koşan. Extensions of rings having McCoy condition. Cambridge University Press (2009)
  • W. Krull. Allgemeine Bewertungstheorie. (1932)
  • T.-Y. Lam. A crash course on stable range, cancellation, substitution and exchange. World Scientific (2004)
  • T.-Y. Lam. A first course in noncommutative rings. Springer Science \& Business Media (2013)
  • T.-Y. Lam. Exercises in modules and rings. Springer Science \& Business Media (2007)
  • T.-Y. Lam. Lectures on modules and rings. Springer Science \& Business Media (2012)
  • T. Lam and A. S. Dugas. Quasi-duo rings and stable range descent. Elsevier (2005)
  • J. Lambek. Lectures on rings and modules. American Mathematical Soc. (2009)
  • M. D. Larsen and P. J. McCarthy. Multiplicative theory of ideals. Academic press (1971)
  • J. Lawrence. A countable self-injective ring is quasi-Frobenius. JSTOR (1977)
  • J. Lawrence. Erratum to:“A countable self-injective ring is quasi-Frobenius”(Proc. Amer. Math. Soc. 65 (1977), no. 2, 217--220). (1979)
  • T.-K. Lee, Z. Yi, and Y. Zhou. An example of Bergman's and the extension problem for clean rings. Taylor \& Francis (2008)
  • L. Levy. Commutative rings whose homomorphic images are self-injective. Mathematical Sciences Publishers (1966)
  • H. Lombardi and C. Quitt\'e. Commutative algebra: Constructive methods: Finite projective modules. Springer (2015)
  • K. A. Loper. Almost Dedekind domains which are not Dedekind. Springer (2006)
  • S. R. Lopez-Permouth. Rings of Quotients. North Carolina State University (1985)
  • M. Lorenz. K0 of skew group rings and simple noetherian rings without idempotents. Oxford University Press (1985)
  • A. Malcev. On the immersion of an algebraic ring into a field. Springer (1937)
  • G. Marks. Duo rings and Ore extensions. Elsevier (2004)
  • G. Marks. On 2-primal Ore extensions. Taylor \& Francis (2001)
  • G. Marks. Reversible and symmetric rings. Elsevier (2002)
  • G. Marks. Skew polynomial rings over 2-primal rings. Taylor \& Francis (1999)
  • J. Marot. Une g{\'e}n{\'e}ralisation de la notion danneau de valuation. (1969)
  • E. Matlis. Rings of type I. Elsevier (1972)
  • E. Matlis and others. The minimal prime spectrum of a reduced ring. University of Illinois at Urbana-Champaign, Department of Mathematics (1983)
  • H. Matsumura. Commutative algebra. WA Benjamin (1970)
  • H. Matsumura. Commutative ring theory. Cambridge university press (1989)
  • J. C. McConnell, J. C. Robson, and L. W. Small. Noncommutative {N}oetherian rings. American Mathematical Soc. (2001)
  • N. H. McCoy. Remarks on divisors of zero. Taylor \& Francis (1942)
  • W. W. McGovern. Clean semiprime f-rings with bounded inversion. Taylor \& Francis (2003)
  • G. O. Michler and O. Villamayor. On rings whose simple modules are injective. Elsevier (1973)
  • A. V. Mikhalev and G. F. Pilz. The concise handbook of algebra. Springer Science \& Business Media (2013)
  • P. J. Morandi, B. A. Sethuraman, and J.-P. Tignol. Division algebras with an anti-automorphism but with no involution. (2005)
  • W. Munn. Simple contracted semigroup algebras. (1978)
  • M. Nagata. Local rings. RE Krieger Pub. Co. (1962)
  • M. Nagata and others. An example of a normal local ring which is analytically reducible. Kyoto University (1958)
  • T. Nakayama. On Frobeniusean algebras. I. JSTOR (1939)
  • C. Nastasescu and N. Popescu. Anneaux semi-artiniens. (1968)
  • W. K. Nicholson. Lifting idempotents and exchange rings. (1977)
  • W. K. Nicholson. Semiregular modules and rings. Cambridge University Press (1976)
  • W. K. Nicholson. Strongly clean rings and Fitting's lemma. Taylor \& Francis (1999)
  • W. K. Nicholson. 𝐼-rings. (1975)
  • W. K. Nicholson and M. F. Yousif. Annihilators and the CS-condition. Cambridge University Press (1998)
  • W. K. Nicholson and M. F. Yousif. Principally injective rings. Elsevier (1995)
  • W. K. Nicholson and M. F. Yousif. Quasi-Frobenius Rings. Cambridge University Press (2003)
  • W. K. Nicholson and M. Yousif. On dual rings. (1999)
  • W. K. Nicholson and M. Yousif. Weakly continuous and C2-rings. Taylor \& Francis (2001)
  • W. Nicholson and M. Yousif. On perfect simple-injective rings. (1997)
  • W. K. Nicholson and Y. Zhou. Clean rings: a survey. World Scientific (2005)
  • W. Nicholson, J. Park, and M. Yousif. On simple-injective rings. (2002)
  • P. Nielsen. Symmetry of unique generator property. (2022)
  • P. P. Nielsen. Semi-commutativity and the {M}c{C}oy condition. Academic Press (2006)
  • P. P. Nielsen and J. Ster. Connections between unit-regularity, regularity, cleanness, and strong cleanness of elements and rings. (2015)
  • J.-I. Nishimura. A few examples of local rings, I. Duke University Press (2012)
  • N. C. Norton. Generalizations of the theory of quasi-frobenius rings. (1975)
  • K. C. O'Meara. The exchange property for row and column-finite matrix rings. Elsevier (2003)
  • O. Ore. Theory of non-commutative polynomials. JSTOR (1933)
  • B. L. Osofsky. A generalization of quasi-Frobenius rings. Elsevier (1966)
  • B. L. Osofsky. Rings all of whose finitely generated modules are injective. Mathematical Sciences Publishers (1964)
  • K. C. O’Meara. A new setting for constructing von Neumann regular rings. Taylor \& Francis (2017)
  • D. S. Passman. Observations on group rings. Taylor \& Francis (1977)
  • G. A. Pino, K. M. Rangaswamy, and M. S. Molina. Weakly regular and self-injective Leavitt path algebras over arbitrary graphs. Springer (2011)
  • G. Puninski. Projective modules over the endomorphism ring of a biuniform module. Elsevier (2004)
  • G. Puninski. Serial rings. Springer Science \& Business Media (2001)
  • Y. Quentel. Sur la compacit{\'e} du spectre minimal d’un anneau. (1971)
  • J. Ram. On the semisimplicity of skew polynomial rings. (1984)
  • M. B. Rege, S. Chhawchharia, and others. Armendariz rings. The Japan Academy (1997)
  • M. Reid. Akizuki's counterexample. (1995)
  • G. Renault. Sur les anneaux de groupes. (1971)
  • F. Rohrer. Irreducibility and integrity of schemes. Elsevier (2015)
  • C. Rotthaus. Nicht ausgezeichnete, universell japanische Ringe. Springer (1977)
  • L. Rowen. Ring Theory V1. Elsevier Science (1988)
  • E. A. Rutter and Jr. Rings with the principal extension property. Taylor \& Francis (1975)
  • P. Samuel. On unique factorization domains. Duke University Press (1961)
  • F. Sandomierski. Linearly compact modules and local Morita duality. Elsevier (1972)
  • O. F. G. Schilling. Ideal theory on open Riemann surfaces. (1946)
  • R. C. Schwiebert. Semi-Noetherian modules: epilogue. (2023)
  • J. C. Shepherdson. Inverses and zero divisors in matrix rings. Citeseer (1951)
  • T. S. Shores and R. Wiegand. Rings whose finitely generated modules are direct sums of cyclics. Academic Press (1974)
  • L. W. Small. Hereditary rings. National Acad Sciences (1966)
  • J.-P. Soublin. Anneaux et modules coh{\'e}rents. Academic Press (1970)
  • J. Ster. Corner rings of a clean ring need not be clean. Taylor \& Francis (2012)
  • J. Ster. Lifting units in clean rings. Elsevier (2013)
  • J. Ster. The clean property is not a Morita invariant. Elsevier (2014)
  • R. G. Swan. K-theory of coherent rings. (2019)
  • A. A. Tuganbaev. Left and right distributive rings. Springer (1995)
  • A. A. Tuganbaev. Rings close to regular. Springer Science \& Business Media (2013)
  • A. A. Tuganbaev. Semidistributive modules and rings. Springer Science \& Business Media (2012)
  • A. A. Tuganbaev. Semiregular, weakly regular, and $\pi$-regular rings. Springer (2002)
  • Y. Utumi. On continuous rings and self injective rings. JSTOR (1965)
  • P. V\'amos. The Decomposition of Finitely Generated Modules and Fractionally Self-Injective Rings. Wiley Online Library (1977)
  • K. Varadarajan. Hopfian and co-Hopfian objects. JSTOR (1992)
  • W. V. Vasconcelos. Finiteness in projective ideals. Elsevier (1973)
  • R. Ware. Endomorphism rings of projective modules. (1971)
  • R. Warfield. Bezout rings and serial rings. Taylor \& Francis (1979)
  • R. Wisbauer. Foundations of module and ring theory. Routledge (2018)
  • H.-P. Yu. On quasi-duo rings. Cambridge University Press (1995)
  • A. Zalesskii and O. Neroslavskii. There exist simple Noetherian rings with zero divisors but without idempotents. MARCEL DEKKER INC 270 MADISON AVE, NEW YORK, NY 10016 (1977)
  • O. Zariski and P. Samuel. Commutative algebra. (1958)
  • D. Zelinsky. Linearly compact modules and rings. JSTOR (1953)
  • S. P. contributors. \textit{Stacks Project}. (2018)
  • n. contributors. nLab. (2020)