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Modules over some group rings, having d-generator property

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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.

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Authors and Affiliations

  1. UAEU, Al-Ain, United Arab Emirates

    V. A. Bovdi

  2. Department of Algebra and Geometry, School of Mathematics and Mechanics, National University of Dnipro, Dnipro, Ukraine

    L. A. Kurdachenko

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  1. V. A. Bovdi
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  2. L. A. Kurdachenko
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Correspondence to V. A. Bovdi.

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The research was supported by the UAEU UPAR Grant G00002160.

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Bovdi, V.A., Kurdachenko, L.A. Modules over some group rings, having d-generator property. Ricerche mat 71, 135–145 (2022). https://doi.org/10.1007/s11587-021-00581-5

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