Existence of covering topological R-modules | Zendy

Nazmiye Alemdar | Zendy; Osman Mucuk | Zendy

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Existence of covering topological R-modules

Author(s) -

Nazmiye Alemdar,

Osman Mucuk

Publication year - 2013

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1306121a

Subject(s) - mathematics , cover (algebra) , covering space , morphism , topological group , topology (electrical circuits) , singleton , path (computing) , group (periodic table) , fundamental group , topological space , identity (music) , discrete group , combinatorics , discrete mathematics , pure mathematics , computer science , mechanical engineering , pregnancy , chemistry , physics , organic chemistry , biology , acoustics , engineering , genetics , programming language

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 ∈ M be the identity element of the additive group structure of M, and N a submodule of the R-module π1(M,0). In this paper we prove that if R is discrete, then there exists a covering morphism p: (e MN, ˜ 0) → (M,0) of topological R-modules with characteristic group N and such that the structure of R-module on M lifts to e MN. In particular, if N is a singleton group, then this cover becomes a universal cover.

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