Modules over some group rings having d-generator property

DOI10.1007/S11587-021-00581-5arXiv2104.04185MaRDI QIDQ6364873

Publication date: 9 April 2021

Abstract: For modules over group rings we introduce the following numerical parameter. We say that a module A over a ring R has finite r-generator property if each f.g. (finitely generated) R-submodule of A can be generated exactly by r elements and there exists a f.g. R-submodule D of A, which has a minimal generating subset, consisting exactly of r elements. Let FG be the group algebra of a finite group G over a field F. In the present paper modules over the algebra FG having finite generator property are described.

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Special subgroups (Frattini, Fitting, etc.) (20D25) Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras) (16D70) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Other classes of modules and ideals in associative algebras (16D80) General module theory in associative algebras (16D10)

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