A natural partial order for semigroups
A natural partial order for semigroups
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DOI：
10.1090/s0002-9939-1986-0840614-0
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发表时间：
1986-03
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影响因子：
--
通讯作者：
H. Mitsch
中科院分区：
文献类型：
--
作者：
H. Mitsch
半群（S，）上的偏序称为自然序，如果它是由S的乘法定义的。本文证明了对任意半群（S，1），关系a < B当且仅当a = x B = by，xa = a，x，y ∈ S，1是偏序.它与Hartwig [4]和Nambooripad [10]定义的正则半群的自然偏序一致。研究了集合X上所有映射在正则半群（Tx，o）上的自然偏序所导出的相似关系。
A partial order on a semigroup (S, ) is called natural if it is defined by means of the multiplication of S. It is shown that for any semigroup (S, ) the relation a < b iff a = xb = by, xa = a for some x,y E S1, is a partial order. It coincides with the well-known natural partial order for regular semigroups defined by Hartwig [4] and Nambooripad [10]. Similar relations derived from the natural partial order on the regular semigroup (Tx, o) of all maps on the set X are investigated.