Some ranks of modules over group rings
V.A. Bovdi, L.A. Kurdachenko
TL;DR
This paper explores the properties of modules over group rings, extending concepts like finite rank and the r-generator property from commutative rings to modules, and examining their relation to Pr"ufer domains.
Contribution
It introduces analogs of finite rank and the r-generator property for modules over group rings, expanding the understanding of their structure and relation to Pr"ufer domains.
Findings
Defined module analogs of finite rank and r-generator property
Established connections between these module properties and Pr"ufer domains
Provided new insights into the structure of modules over group rings
Abstract
A commutative ring R has finite rank r, if each ideal of R is generated at most by r elements. A commutative ring R has the r-generator property, if each finitely generated ideal of R can be generated by r elements. Such rings are closely related to Pr\"ufer domains. In the present paper we investigate some analogs of these concepts for modules over group rings.
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Taxonomy
TopicsRings, Modules, and Algebras · Finite Group Theory Research · Algebraic structures and combinatorial models