(to be added) The ring $R$ has the property that there exists a f.g. projective $R$ module $M$ and a module $N$ such that in the monoid of isomorphism classes of $R$ modules, $[M]+[N]=[R]=[R]+[R]$.

- G. M. Bergman. Coproducts and some universal ring constructions. (1974) @ (Fixme)
- T.-Y. Lam. Exercises in modules and rings. (2007) @ Exercise 18.11, pp 362-363

Symmetric properties

Asymmetric properties

Legend

- = has the property
- = does not have the property
- = information not in database

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