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

Keywords:

• Dedekind domain
• module over ring
• Prüfer domain
• special rank

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 20C05
• 20F50
• Secondary: 20D25
• 16D10
• 16D70
• 16D80

Acknowledgment

We would like to express our deep gratitude to the referee for the thoughtful and constructive review of our manuscript.

Additional information

Funding

This research was supported by the UAEU UPAR Grant G00002160.