Throughout this paper we assume that all modules are finitely generated (left) modules over
a noetherian R-algebra A for a commutative local ring R. By a noetherian R-algebra A, we …

Module theory is an important tool for many different branches of mathematics, as well as
being an interesting subject in its own right. Within module theory, the concept of injective …

A submodule A of a left module B (over an associative ring with 1) is pure if for any right
module F, the natural homomorphism F⊗ A→ F⊗ B is injective. A module C is pure-injective …

Modules which are extending relative to module classes Page 1 COMMUNICATIONS IN
ALGEBRA, 26(6), 1699- 172 1 (1998) MODULES WHICH ARE EXTENDING RELATIVE TO …

Let R be a commutative Noetherian ring and M a finitely generated R-module. Under various
hypotheses, it is proved that the center of End R (M) coincides with the endomorphism ring …

In a celebrated theorem, AW Goldie determined necessary and sufficient conditions that a
ring have a left quotient ring which is semisimple with minimum condition [4]. Our first main …

The fimdam al result of AV Jategaonkar's im ortant paper is th, e following: If is a finitely
generated Noetherian ring, and) r is an essential submoduie of ml! dimens~ Q~ 4.2, then M …

Let R be a ring with identity element and M be a unitary left R-module. M is called quasi-
injective if every element in Hom^ Af, M) for any R-module N in M is extened to an element in …

In this paper necessary and sufficient conditions are obtained for a direct sum⊕ α∈ JA α of
R-modules to be M. injective in the sense of Azumaya. Using this result it is shown that if {A …

Let R be a ring with identity and let be a finite direct sum of relatively protective R-modules
Mi Then it is proved that M is lifting if and only if M is amply supplemented and Mi is lifting for …