弱交换富足序半群(Ⅰ)  

On Weakly Commulation Abundant Po-Semigroups(Ⅰ)

作　　者：高振林 

机构地区：[1]上海市扬浦区教育学院,上海200093

出　　处：《数学学报（中文版）》2001年第4期693-700,共8页Acta Mathematica Sinica：Chinese Series

摘　　要：本文将序半群上的 Ｇｒｅｅｎ’ｓ－关系推广为 Ｇｒｅｅｎ’ｓ＊一关系．给出主序（左、右）＊－理想、主序＊－滤特征描述和弱交换富足序半群的特征．用这些特征证明了一类弱交换富足序半群的结构定理：若序半群Ｓ满足 ，则Ｓ是弱交换富足序半群当且仅当Ｓ是左（右）单序半群｛（ｅ）（Ｓ）｝的半格．Green's *-relations on po-semigroups and abundant po-semigroups are introduced and studied. By using these results, we show that the structure theorem of weakly commutative abundant po-semigroups as follows: If N then S is a weakly commutative abundant po-semigroup if and only if S is a semilattice of left (resp. right) simple semigroups {(e)), for some (s),

关 键 词：Green's＊关系 弱交换富足序半群 主序-理想 左单序半群半格 右单序半群半格 序半群 序半格同余 

分 类 号：O152.7[理学—数学]