Name: Davenport constant for commutative rings
Creator: Deng, Calvin
Keywords: finite rings, Semigroup rings, multiplicative semigroups of rings, Davenport constant, Group Theory (math.GR), Mathematics - Commutative Algebra, Commutative Algebra (math.AC), 16. Peace & justice, 01 natural sciences, Commutative semigroups, 13. Climate action

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2017Embargo end date: 01 Jan 2016 English Publisher:Elsevier BVJournal:Journal of Number Theory, volume 172, pages 321-342 (issn: 0022-314X,

Authors: Deng, Calvin;

doi: 10.1016/j.jnt.2016.08.001 , 10.48550/arxiv.1602.03445

arXiv: 1602.03445

Davenport constant for commutative rings

- Summary
- Subjects
- Metrics

Abstract

The Davenport constant is one measure for how "large" a finite abelian group is. In particular, the Davenport constant of an abelian group is the smallest $k$ such that any sequence of length $k$ is reducible. This definition extends naturally to commutative semigroups, and has been studied in certain finite commutative rings. In this paper, we give an exact formula for the Davenport constant of a general commutative ring in terms of its unit group.

17 pages + 1 page of references

Keywords

finite rings, Semigroup rings, multiplicative semigroups of rings, Davenport constant, Group Theory (math.GR), Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Commutative semigroups, semigroup, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Divisibility and factorizations in commutative rings, Mathematics - Group Theory

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	5
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average