富足半群上的自然偏序

本文研究富足半群上的自然偏序，得到Green关系和自然偏序之间的联系，确定了富足半群何时关于自然偏序具有单边(双边)相容，另外，也研究了富足半群的本原元。  

On the Construction of Regular Orthocryptogroups

The aim of this paper is to study regular orthocryptogroups. After obtaining some characterizations of such semigroups, we establish the construction theorem of regular orthocryptogroups. As an application, we give the construction theorem of right quasi-normal orthocryptogroups and study homomorphisms between two regular orthocryptogroups. Received September 24, 1999, Accepted May 9, 2001  

逆半群半格上的自然偏序关系

首先讨论逆半群Sa的半上的自然偏序与各Sa上的自然偏序之间的关系，然后讨论逆半群Sa的半格S的幂等元集Ea的闭包限制在Sa上与Ea的闭包的关系．  

自然序Dubreil-Jacotin富足半群

本文考虑Ｄｕｂｒｅｉｌ－Ｊａｃｏｔｉｎ富足半群，给出若干特征后，建立了自然序Ｄｕｂｒｅｉｌ－Ｊａｃｏｔｉｎ富足半群的结构，作为应用，给出了具有正则性条件的自然序Ｄｕｂｒｅｉｋｌ－Ｊａｃｏｔｉｎ富足半群的结构，并将结果推广到具有最大幂等元的自然序的偏序富足半群上。  

A relation for general and inverse semigroups

The relation in the title is S defined by

Characterizing cryptogroups with a finite number of $${\mathcal{H}}$$ -classes in each $${\mathcal{D}}$$ -class by their subsemigroups

We construct a family of completely regular semigroups with the property that each completely regular semigroup S with a finite number of -classes in each -class is non-cryptic if and only if S contains an isomorphic image of a member of . Each member F of is an ideal extension of a Rees matrix semigroup J by a cyclic group B with a zero adjoined and the identity of B is the identity of F. Here with I and Λ finite, G is given by generators and relations, and P is given explicitly. Within completely regular semigroups, the cryptic property is equivalent to where is the natural partial order and a if and only if a ² = ab = ba. Hence the above result can be formulated in terms of and .   

正规密码(H)-富足半群

将Green关系推广到Green～-关系。给出了密码^ ～ H-富足半群的半格分解,利用此分解,证明了^ ～ H-富足半群为正规密码^H-富足半群当且仅当它是完全^ ～ H-单半群的强半格.  

F-Monoids

A semigroup S is called F-monoid if S has an identity and if there exists a group congruence ρ on S such that each ρ-class of S contains a greatest element with respect to the natural partial order of S (see Mitsch, 1986 Mitsch , H. ( 1986 ). A natural partial order for semigroups . Proc. Amer. Math. Soc. 97 : 384 – 388 .[Crossref], [Web of Science ®] , [Google Scholar]). Generalizing results given in Giraldes et al. (2004 Giraldes , E. , Marques-Smith , P. , Mitsch , H. ( 2004 ). F-regular semigroups . J. Algebra 274 : 491 – 510 .[Crossref], [Web of Science ®] , [Google Scholar]) and specializing some of Giraldes et al. (Submitted Giraldes , E. , Marques-Smith , P. , Mitsch , H. F-semigroups. Submitted . [Google Scholar]) five characterizations of such monoids S are provided. Three unary operations “∗”, “○”, and “ − ” on S defined by means of the greatest elements in the different ρ-classes of S are studied. Using their properties a charaterization of F-monoids S by their regular part S° = {a°|a ∊ S} and the associates of elements in S° is given. Under the hypothesis that S ^∗ = {a ^∗|a ∊ S} is a subsemigroup it is shown that S is regular, whence of a known structure (see Giraldes et al., 2004 Giraldes , E. , Marques-Smith , P. , Mitsch , H. ( 2004 ). F-regular semigroups . J. Algebra 274 : 491 – 510 .[Crossref], [Web of Science ®] , [Google Scholar]).