Modules over some group rings, having d-generator property

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 mini...

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Bibliographic Details
Published in:Ricerche di matematica 2022-06, Vol.71 (1), p.135-145
Main Authors: Bovdi, V. A., Kurdachenko, L. A.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Fields (mathematics)
Geometry
Group theory
Mathematics
Mathematics and Statistics
Modules
Numerical Analysis
Probability Theory and Stochastic Processes
Rings (mathematics)
Set theory
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Summary: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.
ISSN:0035-5038
1827-3491
DOI:10.1007/s11587-021-00581-5