Abstract
An ω1-separable p-group is an abelian p-group such that every countable subset is contained in a countable Σ-cyclic summand. Our goal is to study the endomorphism ring, E(A) , of such a group, A , of cardinality ω l, in the spirit of Pierce [P] and Corner [C], who investigated E(A) , for arbitrary separable A , modulo the ideal Es(A) of small endomorphisms. Their work, together with later work of Dugas-Göbel [DG] and Shelah [Sh],provided realizability theorems for E(A)/Es(A) . (All the results are theorems of ZFC). In particular, [DG] and [Sh] construct a family of groups realizing a given ring which is rigid in the sense that all homomorphisms between two different members of the family are small.
Research supported by NSF Grant No. MCS80-03591E.
Research supported by National Science and Engineering Research Council of Canada, Grant No. U0075
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Eklof, P.C., Mekler, A.H. (1983). On Endomorphism Rings of ω1-Separable Primary Groups. In: Göbel, R., Lady, L., Mader, A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 1006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21560-9_16
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DOI: https://doi.org/10.1007/978-3-662-21560-9_16
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