On the compatibility of the natural order on a regular semigroup
On the compatibility of the natural order on a regular semigroup
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正则半群上自然序的相容性
DOI：
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发表时间：
1983
期刊：
影响因子：
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通讯作者：
G. Gomes
中科院分区：
文献类型：
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作者：
T. Blyth;G. Gomes
一个显着的成就，代数理论的半群已发现Nambooripad的自然秩序的一个正规半群。他已经表明，这个顺序是兼容的乘法当且仅当半群是局部逆，在这个意义上说，每一个地方submonoid是一个逆半群。在本文中，我们精确地确定了自然序在右（分别在左）与乘法相容的时候;这是如此，当且仅当每个局部子幺半群都是n-幂单的（分别是n-幂单的）。
Synopsis A notable achievement in the algebraic theory of semigroups has been the discovery by Nambooripad of the natural order on a regular semigroup. He has shown that this order is compatible with multiplication if and only if the semigroup is locally inverse, in the sense that every local submonoid is an inverse semigroup. In this paper we determine precisely when the natural order is compatible on the right (respectively left) with multiplication; this is so if and only if every local submonoid is ℒ-unipotent (respectively ℛ-unipotent).