Endomorphism Rings of Faithfully Flat Abelian Groups

A-Projective Resolutions and an Azumaya Theorem for a Class of Mixed Abelian Groups

“…But this yields that A is homogeneous completely decomposable by [1]. Therefore, A ∼ = É n , and all A-solvable groups are A-projective.…”

“…In the second case, it remains to show that A is reduced. If É ⊆ A, then every torsion-free A-generated group is A-solvable as in [1].…”

“…Following [1], we say that an abelian group G is A-solvable if the evaluation map θ G : Hom(A, G) ⊗ E(A) A → G is an isomorphism. Theorem 3.2 and Corollary 3.4 characterize the finitely Agenerated A-solvable groups.…”

The finite quasi-Baer property

“…Although it soon became apparent that some restrictions are needed, it was not until 1975 that Arnold and Lady showed in [11] that the most natural way to introduce these restrictions is in terms of the endomorphism ring, E = E(A), of the group A. Following their approach, Albrecht proved in [6] that the Baer splitting property for a group A is closely connected the structure of A as a left E-module. In this discussion, the faithfulness of A as an E-module played a central role.…”

Abelian groups flat as modules over their endomorphism ring

“…The main emphasis of Section 3 is to use semi-A-closed classes to investigate homological properties of abelian groups A whose endomorphism ring is right coherent. There are a variety of characterizations of right coherent rings R (see Another advantage gained by considering semi-A-closed instead of A-closed classes is that the requirement that A is a faithful E(A)-module does not arise immediately as it did in [4]. On the other hand, dropping this requirement gives rise t o other problems.…”