One-to-One Partial Right Translations of a Right Cancellative Semigroup
One-to-One Partial Right Translations of a Right Cancellative Semigroup
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DOI：
10.1016/0021-8693(76)90158-7
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发表时间：
1976-11
影响因子：
0.9
通讯作者：
D. Mcalister
中科院分区：
文献类型：
--
作者：
D. Mcalister
半群S的一对一部分右平移是整环为左理想的S的一对一部分变换p，它的性质是对每个aEap，xEs，(Xa)p=x(Ap).S的所有一对一部分右平移的集合3是一个逆半群，它反映了S的许多性质。9的构造产生了一个从半群范畴到逆半群范畴的函子。前两节分别讨论了这个函子对对象和态射的影响。第三节利用函子证明了右可消么半群范畴和所谓的允许同态范畴自然等价于一个O-单逆半群范畴。明确地刻画了O-单逆半群范畴。这一结果类似于Clifford定理，Clifford定理用右单位子半群描述了双单逆么半群的结构。
A one-to-one partial right translation of a semigroup S is a one-to-one partial transformation p of S whose domain is a left ideal and which has the property that for each a E Ap, x ES,(xa) p= x (ap). The set 3 of all one-to-one partial right translations of S is an inverse semigroup which reflects many of the properties of S. The construction of 9 gives rise to a functor from a category of semigroups to the category of inverse semigroups. The first two sections deal with the effect of this functor on objects and morphisms respectively. In the third section, the functor is applied to show that the category of right cancellative monoids and, so-called, permissible homomorphisms is naturally equivalent to a category of O-simple inverse semigroups. The category of O-simple inverse semigroups is explicitly described. This result can be considered as an analog to Clifford’s theorem which describes the structure of a bisimple inverse monoid in terms of its right unit subsemigroup.