NonNoetherian Commutative Ring Theory pp 387402  Cite as
ERings and Related Structures
Abstract

[19] A torsionfree abelian group G is cyclic and projective as a module over its endomorphism ring if and only if G = R ⊕ M, where R is an Ering and M is an Emodule over R.

[27] A strongly indecomposable torsionfree abelian group G of finite rank is finitely generated over its endomorphism ring if and only if G is quasiisomorphic to the additive group of an Ering.

[15] A strongly indecomposable torsionfree group G of finite rank is uniserial as a module over its endomorphism ring only if G is a local, strongly homogeneous Ering.

[2] A universal algebra A is κfree if there is a subset X of A of car dinality κ such that every function from X to A extends uniquely to an endomorphism of A. A ring that is lfree as an abelian group is precisely an Ering (with X = {1}).
Keywords
Abelian Group Galois Group Galois Extension Endomorphism Ring Finite RankPreview
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