Weighted Erdős-Burgess and Davenport constant in commutative rings

2022/02/24 by Guoqing Wang, Wang, Guoqing
Mathematics · #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2202.11887

openalex publication_date 2022/02/24 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Let R be a finite commutative unitary ring. An idempotent in R is an element e∈ R with e²=e. Let Ψ be a subgroup of the group \rm Aut(R) of all automorphisms of R. The Ψ-weighted Erdős-Burgess constant \rm I_Ψ(R) is defined as the smallest positive integer ℓ such that every sequence over R of length at least ℓ must contain a nonempty subsequence a₁,…, a_r such that ∏_i=1^r ψ_i(a_i) is one idempotent of R where ψ₁,…,ψ_r∈ Ψ. In this paper, for the finite quotient ring of a Dedekind domain R, a connection is established between the Ψ-weighted-Erdős-Burgess constant of R and the Ψ-weighted Davenport constant of its group of units by all the prime ideals of R.

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