Different and distinct notions of regularity for modules exist in the literature. When these
notions are restricted to commutative rings, they all coincide with the well-known von …

Regular rings were originally introduced by John von Neumann to clarify aspects of operator
algebras ([33],[34],[9]). A continuous geometry is an indecomposable, continuous …

We study modules whose endomorphism rings possess various forms of von Neumann
regularity. We characterize these “regularity” properties for several classes of modules …

Jayaram and Tekir defined an R-module M, R is a commutative ring, to be “von Neumann
regular” if for each m∈ M, there exists an a∈ R such that R m= a M= a 2 M. Previously …

ON REGULARITY OF RINGS 1 Page 1 ON REGULARITY OF RINGS 1 Jianlong Chen Department
of Mathematics, Harbin Institute of Technology Harbin 150001, PR China and Department of …

A note on regular modules Page 1 BULL. AUSTRAL. MATH. SOC. I6A30 VOL. II ( 1 9 7 4 ) , 3 5
9 - 3 6 4 . ( I 6 A 5 O ) A note on regular modules VS Ramamurthi Kaplansky's observation …

The themes of cancellation, internal cancellation, substitution and exchange have led to a lot
of interesting research in the theory of modules over commutative and noncommutative …

A submodule A of a left module B (over an associative ring with 1) is pure if for any right
module F, the natural homomorphism F⊗ A→ F⊗ B is injective. A module C is pure-injective …

The notion of purity is extremely important in abelian group theory. One reason for this is that
there are enough pure-injective (and also enough pure-projective) groups, which makes it …

For a ring R, call a class C of R-modules (pure-) mono-correct if for any M, N∈ C the
existence of (pure) monomorphisms M→ N and N→ M implies M≃ N. Extending results and …