Modules invariant under automorphisms of their covers and envelopes

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Guil Asensio P. A., Tutuncu D. K., Srivastava A. K.

ISRAEL JOURNAL OF MATHEMATICS, vol.206, no.1, pp.457-482, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 206 Issue: 1
  • Publication Date: 2015
  • Doi Number: 10.1007/s11856-014-1147-3
  • Journal Name: ISRAEL JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.457-482
  • Hacettepe University Affiliated: Yes

Abstract

In this paper we develop a general theory of modules which are invariant under automorphisms of their covers and envelopes. When applied to specific cases like injective envelopes, pure-injective envelopes, cotorsion envelopes, projective covers, or flat covers, these results extend and provide a much more succinct and clear proofs for various results existing in the literature. Our results are based on several key observations on the additive unit structure of von Neumann regular rings.