… the regular graph of R. In this paper, we generalize the regular graph of R to the M-regular …
It is the undirected graph with all M-regular elements of R as vertices, and two distinct vertices …

… regular ring all projective left and right modules are regular (see [13, Lemma 41 or [7, Theorem
1.11 I). A variety of examples of regular modules over non regular rings … commutative ring …

… of the sort we have in mind: a ring of operators on a module over a commutative algebra. …
and s g R is regular then s s 0 implies that s ) M s s ) M s 0. Since M is flat as an R-module, …

… We also prove, among other things, that if R is a commutative ring and M is a finitely … And
since submodules of regular modules are again regular we conclude that I is semisimple by …

… , determinants, modules over commutative rings, as well as the definition of quotient and …
rings. A familiarity with polynomial rings, the arithmetic properties of Z and Euclidian rings is …

… We provide a precise description of an indecomposable endoregular module over an arbitrary
commutative ring. A structure theorem for extending an endoregular abelian group is also …

… We show that a PI-ring R is left perfect if and only if all left R-modules have maximal … , for
commutative rings injectivity of all completely reducible modules is equivalent to the ring being …

… In Section 2, we show that a ring R is a regular … ring if and only if every finitely generated
torsion R-module is of finite … that a torsion module over a regular multiplication ring is a direct …

… Rings whose simple singular modules are injective are studied in [1] and [4], In particular, it
… 3.6] that a commutative ring R is regular iff every simple singular R-module is injective. In this …

… a new proof of this result in the case when R is a regular local ring. By [7], the general case is
… R be a commutative ring, let M and N be two R-modules, and let I be an injective R-module. …