Endomorphism rings of modules whose cardinality is cofinal to omega

2000/11/22 by Rüdiger Göbel, Saharon Shelah
Mathematics · #math.RA #math.LO

paper · pdf

published as Abelian groups, module theory, and topology (Padua, 1997), volume 210 of Lecture Notes in Pure and Appl. Math., pp 235-248, Dekker, New York, 1998

arxiv created 2000/11/22 · arxiv updated 2009/11/30

Abstract

The main result is Theorem: Let A be an R-algebra, mu, lambda be cardinals such that |A|<=mu=mu^aleph₀<lambda<=2^mu. If A is aleph₀-cotorsion-free or A is countably free, respectively, then there exists an aleph₀-cotorsion-free or a separable (reduced, torsion-free) R-module G respectively of cardinality |G|=lambda with End_RG=A oplus Fin G.

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