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Similarities and differences between Abelian groups and modules over non- perfect rings. (English) Zbl 0823.20060

Göbel, Rüdiger (ed.) et al., Abelian group theory and related topics. Conference, August 1-7, 1993, Oberwolfach, Germany. Providence, RI: American Mathematical Society. Contemp. Math. 171, 397-406 (1994).
The author looks into the notions of a Whitehead test module, an almost free module, and a slender module, over non-perfect rings, in the category of unitary left \(R\)-modules. This is done from the standpoint of comparison with results in abelian group theory in order to answer (the author’s) questions as to what results generalize straightforwardly.
The title of the paper and the author’s intent are somewhat of a misnomer, at least regarding the slender property, for the reviewer has shown [Abelian group theory, Proc. Conf., Honolulu 1983, Lect. Notes Math. 1006, 375-383 (1983; Zbl 0517.18013)] that the notion of slenderness generalizes to a wide class of abelian categories.
For the entire collection see [Zbl 0801.00024].

MSC:

20K40 Homological and categorical methods for abelian groups
20K35 Extensions of abelian groups
16P70 Chain conditions on other classes of submodules, ideals, subrings, etc.; coherence (associative rings and algebras)
18E10 Abelian categories, Grothendieck categories
16E60 Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc.

Citations:

Zbl 0517.18013
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