Throughout this paper we assume that all rings are commutative, noetherian rings with unit
and that all modules are finitely generated and unitary. The main object of study is what it …

This paper proves a partial converse to the Krull-Schmidt theorem for HenseI local rings and
a cancellation result for modules in terms of the endomorphism ring of the module. The …

This is a study of the conditions under which smallness of proper submodules will influence
the structure of the endomorphism ring of a module. The case in which that endomorphism …

Introduction In 1 we discuss the structure of Tor (K, K) when R is a commutative, noetherian
ring, and K is a homomorphic image of R which is a field. If we view K as an R-module …

Introduction. This paper is devoted primarily to the study of commuta-tive noetherian local
rings. The main task is to compare purely algebraic properties with properties of a …

The main results of this paper are cancellation, n-th root, and isomorphic refinement
theorems for finitely generated modules over algebras over commutative zero-dimensional …

In recent years there has arisen an interest in algebraic systems with binary compositions of
addition and multiplication satisfying all the ring aXiOm S, save possibly, one of the …

In this paper we will first establish a duality between in jectivity and flatness for modules.
That is: Let E be a faithfully in jective module". Then, for each module A, we have W, dim. A …

By a well-known theorem due to Kaplansky a commutative ring R is von Neumann regular if
and only if every simple R module is injective. In the noncommutative case neither the …

The use of these notations presupposes, in the first case, that M is an A-module of finite
length, and in the second case, that Tor $(M, N) is a module of finite length fori _> j and is 0 …