… We list below the definitions of the five module-theoretic generalizations of commutative
von Neumann regular rings on which we will be focusing, three from the aforementioned past …

… rings are assumed to be commutative with nonzero identity. In 1936, vonNeumann [4] introduced
the definition of a regular von… of von-Neumann regular ring. Element 𝑎 ∈ 𝑅 is called vN-…

… regular module over a commutative ring to a V N-regular module over a ring which is not
necessarily commutative… to MV Nregular if aM = a2M where R is a commutative ring and M is an …

… a commutative ring with … commutative rings will be discussed. The topological indices
related to the degree of vertices and the diameter of the prime ideal graph of the commutative ring …

… 𝜋-regular module which is a generalization of von Neumann … of modules such as von Neumann
regular modules and second … In section 3, we deal with commutativity of localization at a …

… 𝜋-regular module which is a generalization of von Neumann … of modules such as von Neumann
regular modules and second … In section 3, we deal with commutativity of localization at a …

… are achieved by purely module theoretic methods avoiding the … The regular rings were
introduced by John von Neumann in … Having in mind that the prime radical in a commutative ring …

… Generalizing the well-known fact that unit-regular rings are … of the behavior of regular
elements in commutative rings, is to … module-theoretic characterizations of the regular, unit-regular, …

… results on unit-regular rings are generalized. We also provide … the endomorphism ring is a
(von Neumann) regular ring has … also extends Theorem 4.1 in [6] to a module theoretic setting. …

… endomorphism rings possess various forms of von Neumann regularity. We … module-theoretic
generalizations of commutative regular rings that are not connected to endomorphism rings…