An Analogy of Clifford Decomposition Theorem for Abel-Grassmann Groupoids

• 作者: Madad Khan Saima Anis
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 分解定理 阿贝尔 格拉斯 群胚 比喻 阿基米德 广群 正整数
• 年，卷（期）: 2014,（2）
• 页码范围: 347-353
• 页数: 7页
• 分类号: O159
• 语种: 中文

摘要

Let S be an inverse AG-groupoid (Abel-Grassmann groupoid) and define a relation γ on S by aγb if and only if there exist some positive integers n and m such that bm∈ (Sa)S and an∈ (Sb)S. We prove that S/γ is a maximal semilattice homomorphic image of S. Thus, every inverse AG-groupoid S is uniquely expressible as a semilattice Y of some Archimedean inverse AG-groupoids Sα (α∈ Y). Our result can be regarded as an analogy of the well known Clifford theorem in semigroups for AG-groupoids.