逆半直积的推广
Generalization of Inverse Semidirect Products
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摘要: 主要研究了逆半群的半直积及其推广.首先给出了逆半群的半直积,定义了一种新的积——双半直积(它由集合M={(a,s)∈S×T:(a,s)(b,t)=(ab,sbta)}构成,其中sb=sβ(b),ta=ta(a)).然后讨论了半格与纯正半群的双半直积的性质.最后证明了半格与纯正半群的双半直积的是一个纯正半群.
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关键词:
- 半群,半直积,双半直积
Abstract: In this paper,the semidirect products of inverse semigroups are discussed and generalized.First,we con-sider the semidirect products of inverse semigroups and define a new product--the double-semidirect product (It is a set M ={(a,s) ∈S×T:(a,s) (b,t)=(ab,sbta)},where sb = sβ(b),ta(a))).Afterwards,properties of doub-le-semidireet product of a semilattice and an orthodox semigroup are discussed.Finally,we prove that the double-se-midirect product of a semilattice and an orthodox semigroup is an orthodox semigroup. -
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