THEOREM 1. Assumptions.(i) N is finitely presented as A-left-module, EndA (N) finitely
generated as R-module and M a direct summand in a direct sum of finitely presented A …

Proof. For any ring R with identity, it is easy to see that a right ideal/of R is generated by an
idempotent if and only if/is a direct summand of the right iϋ-module RR. If I is an injective …

THE EXISTENCE OF DUAL MODULES JkA + Q Bn = Q (JkA + B„) = JkA + Bn(k) Page 1
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 55, Number 2, March …

We will call an R-module U semiprimary if the ring of multiplications of R on U/rad U is
semisimple with minimum condition and U is finitely generated.(All modules considered in …

We introduce the notion of classical primary submodules that generalizes the concept of
primary ideals of commutative rings to modules. Existence and uniqueness of classical …

Introduction. In this paper several properties of absolutely pure modules are given. It is
shown that absolutely pure and injective are equivalent properties for modules over …

Suppose R is a commutative noetherian ring and M is a finitely generated R-module. If it is
known that all localizations M r of M can be generated by r elements, it is reasonable to look …

A saturated class Δ of modules is any class of nonsingular right 7?-modules closed under
direct sums, injective hulls, submodules and isomorphic copies. Saturated classes are used …

It is clear that this defintion depends on the direct decomposition of T. We have studied a
cyclic hollow module in [3]. We note that the concept dual to a cyclic hollow module is a …

0. Introduction. Let R be a ring. A proper left ideal L of R is prime if, for any elements a and b
in R such that aRb CL, either a€ L or b 6 L. For example, any prime two-sided ideal is a …