# 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)
• T. S. P. Authors. \textit{Stacks Project}. (2018)
• 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. Some examples of non-compressible rings. Taylor \& Francis (1984)
• W. Brandal. Constructing B\'ezout domains. JSTOR (1976)
• 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, W. Nicholson, and M. Yousif. Ikeda--Nakayama rings. Elsevier (2000)
• 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. 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. H. Cozzens. Homological properties of the ring of differential polynomials. (1970)
• R. F. Damiano. A right PCI ring is right Noetherian. (1979)
• 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)
• F. Dischinger and W. Müller. Left PF is not right PF. Taylor \& Francis (1986)
• V. Erdoǧdu. Coprimely packed rings. Elsevier (1988)
• C. C. Faith. Rings and things and a fine array of twentieth century associative algebra. American Mathematical Soc. (2004)
• C. Faith. Lectures on injective modules and quotient rings. Springer (2006)
• C. Faith. Rings with ascending condition on annihilators. Cambridge University Press (1966)
• C. Faith. Subrings of self-injective and FPF rings. Springer (1982)
• C. Faith and S. Page. FPF Ring Theory: Faithful modules and generators of mod-R. Cambridge University Press (1984)
• 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)
• R. W. Gilmer. Multiplicative ideal theory. M. Dekker (1972)
• R. Gilmer and others. On polynomial rings over a Hilbert ring.. The University of Michigan (1971)
• S. Glaz. Commutative coherent rings. Springer (2006)
• 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)
• 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)
• 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)
• 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)
• 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. Rings of operators. Benjamin (1968)
• H. J. Keisler. Elementary calculus: An infinitesimal approach. Courier Corporation (2012)
• 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)
• 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)
• A. Malcev. On the immersion of an algebraic ring into a field. Springer (1937)
• G. Marks. Reversible and symmetric rings. Elsevier (2002)
• 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)
• M. Nagata. Local rings. RE Krieger Pub. Co. (1962)
• T. Nakayama. On Frobeniusean algebras. I. JSTOR (1939)
• W. K. Nicholson. Lifting idempotents and exchange rings. (1977)
• W. K. Nicholson. 𝐼-rings. (1975)
• W. K. Nicholson. Strongly clean rings and Fitting's lemma. Taylor \& Francis (1999)
• 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 Y. Zhou. Clean rings: a survey. World Scientific (2005)
• 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)
• N. C. Norton. Generalizations of the theory of quasi-frobenius rings. (1975)
• 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)
• G. Puninski. Serial rings. Springer Science \& Business Media (2001)
• Y. Quentel. Sur la compacit{\'e} du spectre minimal d’un anneau. (1971)
• M. B. Rege, S. Chhawchharia, and others. Armendariz rings. The Japan Academy (1997)
• G. Renault. Sur les anneaux de groupes. (1971)
• F. Rohrer. Irreducibility and integrity of schemes. Elsevier (2015)
• E. A. Rutter and Jr. Rings with the principal extension property. Taylor \& Francis (1975)
• O. F. G. Schilling. Ideal theory on open Riemann surfaces. (1946)
• 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)
• 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)
• K. Varadarajan. Hopfian and co-Hopfian objects. JSTOR (1992)
• R. Wisbauer. Foundations of module and ring theory. Routledge (2018)
• H.-P. Yu. On quasi-duo rings. Cambridge University Press (1995)
• O. Zariski and P. Samuel. Commutative algebra. (1958)