具有左中心幂等元的完美l-ample半群  

Perfect l-ample semigroups with left central idempotents

作　　者：孙燕[1] 王旭东[1] 任学明[1] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《西北大学学报（自然科学版）》2015年第1期23-27,共5页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(11471255;11326204);陕西省教育厅专项科研计划基金资助项目(14JK1412);校青年基金资助项目(QN1134)

摘　　要：定义完美l-ample半群,并研究具有左中心幂等元的完美l-ample半群的半格分解。利用半格分解,证明了半群S为具有左中心幂等元的完美l-ample半群,当且仅当S为直积Mα×Λα的强半格,其中Mα是右可消幂幺半群,Λα是右零带。这一结果为具有左中心幂等元的完美l-ample半群结构的建立奠定了基础。The concept of perfect 1-ample semigroups is introduced and the semilattice decomposition of perfect 1-ample semigroups with left central idempotents is studied. By using this semilattice decomposition, it is proved that a semigroup S is a perfect 1-ample semigroup with left central idempotents if and only if it is a strong semilattice of a direct product Mα×Λα, where Mα is a right cancellative unipotent monoid and Λα is a right zero band. This result is the basis that the structure theorem of perfect 1-ample semigroups with left central idempotents can be established.

关 键 词：完美l-ample半群 左中心幂等元 强半格 [＊ ~]-格林关系 

分 类 号：O152.7[理学—数学]