… R is a local ring, and E an R-module such that Definition: If R is a commutative ring, we define
the … where E ranges over all finitely generated R-modules of finite homological dimension. …

… -module N offinite type, then Tor M, N) 0 for all j >= i. In this paper we shall prove that for
an arbitrary regular ring R and for two R-modules … regular local ring R and for any two R-modules …

… -regular … ring with a regular commutative graded associated ring, see [6]. The work of [3],
[4] shows that the property (CM) plays an important role in the study of modules over AS-regular …

… module over a regular ring is a multiplicative module. If A is a … of A are cyclic modules over
the corresponding localizations of A… modules over commutative rings are extended to modules …

… rings considered will be commutative rings with identity. We shall consider the consequences
for a ring of the flatness of certain classes of its modules. … ideals of a ring we shall in a real …

… of commutative rings. Finally it is not difficult to see that the answer is affirmative for commutative
rings with … ) elementary divisor ring is an elementary divisor ring, (2) any strongly regular …

… 4-modules with regular singularities when A is a filtered ring satisfying gr(A) is a commutative
g-… If I is an ideal in a commutative ring, r(l) denotes the radical of 1. Finally, "iff" means if and …

… ) that there exists a commutative regular ring which does not … regular rings R of bounded
index. Throughout this paper, R is a ring with identity and R-modules are unitary right f-modules. …

… modules which generalizes that of unit-regular rings. A module is called unit endoregular if its
endomorphism ring is … some results on a unit endoregular module over a commutative ring. …

… rings Ii Regular rings and *-rings. All rings in this paper will be commutative rings with … For
the purpose of this paper the class of regular rings is somewhat too narrow. Remark~ eg~ that …