… Let R be a commutative ring, and let M be an R-module with the property that every cyclic
submodule of M is contained in a projective … If E(M) is a regular ring then M is a regular module. …

… modules over commutative, regular rings. Perhaps the main conclusion of the paper is that
these modules can … modules with almost any pathological property that can be imagined. …

… In this section we let A be a commutative ring, S a multiplicative set of A and M = M(A) be the
collection of maximal ideals mofA. We let Es, Em, Ep, us etc. denote the localization of the y4…

… rings and all commutative regular rings) are distributive; all valuation rings in division rings
and all commutative Dedekind rings … of commutative rings to some wider class of rings (cf. [155…

… A commutative ring is a ring which satisfies the law ab= ba. The element 1 in a … We shall
now show that there exist semiprime rings which are not regular. A commutative ring is called …

… By a regular ring we mean a von Neumann regular ring. For later … wellknown result that
over a regular ring all modules are fiat. … In Proposition 3.8 we show that a commutative ring is …

… a certain commutative (von Neumann) regular ring R associated with each commutative ring
R. … property: every homomorphism from R into a regular ring factors uniquely through φ. The …

… of regular rings which was found independently … K(G) is regular if and only if K is regular and
is uniquely divisible by … G) is regular, then G is a torsion group and K is a regular ring which …

… over a commutative ring R is regular, then every simple … result for general regular modules
over commutative rings. Finally, … For a locally projective module M over a commutative ring R, …

There are different approaches to characterizing the structures of commutative rings: the
category of modules over commutative rings, homology theories, theories of the star operation …