… A if Tor (A, B)= 0 for some Rmodule B, then Tor,(A, B)= 0 for all ji. In fact, if this … regular
local rings, then almost all the results of this paper extend immediately to all regular local rings. …

… simplicial regular local ring resolution … ring, then its completion A is flat as an A-module, so
by the flat base change theorem we have that Lºa º LA Choosing a simplicial regular local ring …

… [13], where he characterized the (von Neumann) regular FGC-rings. In this context the structure
theorem just says that the only regular FGC-rings are the finite direct products of fields. In …

… For an ^4-module M with regular endomorphism ring R we prove that R is unit regular if
and … finite regular ring with identity is unit regular, we produce (Theorem 4) a class of ,4-…

… rings each of whose finitely generated modules is decomposed into a direct sum of distributive
modules (for example, all Artinian serial and Dedekind rings … a commutative regular ring (…

… commutative separable algebras over a commutative ring. Noncommutative separable algebras
have been studied in [2]. Commutative … We recall first that a regular domain is an integral …

… rings the existence of continuous hulls [7] poses a problem. We show that large classes of
commutative rings… , have the property that every continuous module is quasi-injective. We give …

… ring of a finitely generated regular module is a regular ring. Conversely, over a commutative
ring a projective module having a regular … over a commutative ring F the local modules are …

… generators of a module [S]. In the last section we define the notion of a regular prescheme
and … Throughout this paper, R is a commutative ring with identity, and all tensor products and …

… Thus for commutative rings we can write the ring elements on either side. If A … module AA
which is called the right regular module. Analogously, we can construct the left regular module …