Existence of covering topological R-modules

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ALEMDAR N., MUCUK O.

FILOMAT, vol.27, no.6, pp.1121-1126, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 6
  • Publication Date: 2013
  • Doi Number: 10.2298/fil1306121a
  • Journal Name: FILOMAT
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1121-1126
  • Erciyes University Affiliated: Yes

Abstract

Let R be a topological ring with identity and M a topological (left) R-module such that the underlying topology of M is path connected and has a universal cover. Let 0 is an element of M be the identity element of the additive group structure of M, and N a submodule of the R-module pi(1)(M, 0). In this paper we prove that if R is discrete, then there exists a covering morphism p: ((M) over tilde (N), (0) over tilde) -> (M, 0) of topological R-modules with characteristic group N and such that the structure of R-module on M lifts to (M) over tilde (N). In particular, if N is a singleton group, then this cover becomes a universal cover.