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math.RA2000
Endomorphism rings of modules whose cardinality is cofinal to omega
Rüdiger Göbel, Saharon Shelah
The main result is Theorem: Let A be an R-algebra, mu, lambda be cardinals such that |A|<=mu=mu^{aleph_0}<lambda<=2^mu. If A is aleph_0-cotorsion-free or A is countably free, respe…
math.RA2000
Indecomposable almost free modules - the local case
Rüdiger Göbel, Saharon Shelah
Let R be a countable, principal ideal domain which is not a field and A be a countable R-algebra which is free as an R-module. Then we will construct an aleph_1-free R-module G of…
math.RA2000
Clones on regular cardinals
Martin Goldstern, Saharon Shelah
We investigate the structure of the lattice of clones on an infinite set X. We first observe that ultrafilters naturally induce clones; this yields a simple proof of Rosenberg's th…