We study a question raised by Eisenbud, Mustaţa, and Stillman regarding the injectivity of
natural maps from $\Ext $ modules to local cohomology modules. We obtain some positive …

Chapter 1 covers the background necessary for what follows. In particular, general
properties of injectivity and some of its well-known generalizations are stated. Chapter 2 is …

In a recent paper, Menini and Orsatti obtained a theorem ([4], Representation Theorem 3.1)
between categories of modules which extends Fuller's theorem ([1], Theorem 1.1) to a more …

A module M is called an automorphism-invariant module if every isomorphism between two
essential submodules of M extends to an automorphism of M. This paper introduces the …

The paper is a study of modules with a local endomorphism ring. We consider
decompositions of modules and give a simple proof of Azumaya's theorem. We also define …

The use of category equivalences for the study of endomorphism rings stems from the Morita
theorem. In a sense, this theorem can be viewed as stating that if P is a finitely generated …

We use the type theory for rings of operators due to Kaplansky to describe the structure of
modules that are invariant under automorphisms of their injective envelopes. Also, we …

In a recent paper, Holston et al. have defined a module M to be N-subprojective if for every
epimorphism g: B→ N and homomorphism f: M→ N, there exists a homomorphism h: M→ B …

For a category of modules, the notion, dual to that of a torsion radical, has been called a
cotorsion radical. In this paper, the following two properties are examined for a cotorsion …

We continue a study of separable equivalence from (Kadison, Comptes Rendus Math.
Reports Acad. Sci. Canada, 15 (1993) 223–228; Hokkaido Math. J. 24 (1995) 527–549). We …