Categories of Representations of a Class of Commutative Cancellative Semigroups

• 来源期刊: 代数集刊（英文版）
• 学科: 数学
• 关键词: semigroup commutative cancellative subarchimedean category
• 年，卷（期）: 2001,（4）
• 页码范围: 361-380
• 页数: 20页
• 分类号: O1
• 语种: 英文

摘要

A commutative semigroup S is subarchimedean if there exists z ∈ S such that for any a ∈ S, there are n ＞ 0 and x ∈ S such that zn ＝ ax. A commutative cancellative idempotent-free subarchimedean semigroup is a -semigroup.These semigroups admit Tamura-like representations of the form N(G, I) and N(G,ψ), and their groups of quotients Z(G, I) and Z(G, ψ). We consider categories whose objects are of the form (G, I; N), (G, ψ; N), (G, I; Z), and (G, ψ; Z)with suitable morphisms, and establish functorial relationships among these categories as well as with the categories of -semigroups and non-periodic abelian groups.