Some ranks of modules over group rings

Victor A. Bovdi; Leonid A. Kurdachenko

doi:10.1080/00927872.2020.1831007

Some ranks of modules over group rings

Victor A. Bovdi
, Leonid A. Kurdachenko

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 Prüfer domains. In the present paper, we investigate some analogs of these concepts for modules over group rings.

Original language	English
Pages (from-to)	1225-1234
Number of pages	10
Journal	Communications in Algebra
Volume	49
Issue number	3
DOIs	https://doi.org/10.1080/00927872.2020.1831007
Publication status	Published - 2020

Keywords

Dedekind domain
Prüfer domain
module over ring
special rank

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2020.1831007

Cite this

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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{\"u}fer domains. In the present paper, we investigate some analogs of these concepts for modules over group rings.",

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AU - Bovdi, Victor A.

AU - Kurdachenko, Leonid A.

PY - 2020

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N2 - 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 Prüfer domains. In the present paper, we investigate some analogs of these concepts for modules over group rings.

AB - 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 Prüfer domains. In the present paper, we investigate some analogs of these concepts for modules over group rings.

KW - Dedekind domain

KW - Prüfer domain

KW - module over ring

KW - special rank

UR - https://www.scopus.com/pages/publications/85092707926

UR - https://www.scopus.com/pages/publications/85092707926#tab=citedBy

U2 - 10.1080/00927872.2020.1831007

DO - 10.1080/00927872.2020.1831007

M3 - Article

AN - SCOPUS:85092707926

SN - 0092-7872

VL - 49

SP - 1225

EP - 1234

JO - Communications in Algebra

JF - Communications in Algebra

IS - 3

ER -

Some ranks of modules over group rings

Abstract

Keywords

ASJC Scopus subject areas

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