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1.
By an associate inverse subsemigroup of a regular semigroup S we mean a subsemigroup T of S containing a least associate of each x∈S, in relation to the natural partial order ≤
S
. We describe the structure of a regular semigroup with an associate inverse subsemigroup, satisfying two natural conditions.
As a particular application, we obtain the structure of regular semigroups with an associate subgroup with medial identity
element.
Research supported by the Portuguese Foundation for Science and Technology (FCT) through the research program POCTI. 相似文献
2.
For a regular semigroup with an inverse transversal, we have Saito’s structureW(I,S
o, Λ, *, {α, β}). We represent congruences on this kind of semigroups by the so-called congruence assemblage which consist
of congruences on the structure component partsI,S
o and Λ. The structure of images of this type of semigroups is also presented.
This work is supported by Natural Science Foundation of Guangdong Province 相似文献
3.
Group congruences on regular semigroups 总被引:6,自引:0,他引:6
D. R. LaTorre 《Semigroup Forum》1982,24(1):327-340
4.
R-unipotent congruences on regular semigroups 总被引:3,自引:0,他引:3
Gracinda M. S. Gomes 《Semigroup Forum》1985,31(1):265-280
5.
Orthodox congruences on regular semigroups 总被引:4,自引:0,他引:4
Gracinda M. S. Gomes 《Semigroup Forum》1988,37(1):149-166
6.
Robert J. Koch 《Semigroup Forum》1983,26(1):295-305
7.
Amal AlAli 《代数通讯》2017,45(11):4667-4678
8.
正则半群上的矩形群同余 总被引:1,自引:1,他引:1
文[1]中PetrichM定义了同余的核与迹,用它们描述了逆半群上的同余,Gomes在文[2]中定义了同余的核与超迹并描述了正则半群上的R-幂单(R-unipo-tent)同余,本文利用同余的核与超迹描述正则半群上的另一类重要同余,即矩形群同余. 相似文献
9.
黄天霖 《纯粹数学与应用数学》2005,21(3):255-262
研究E-自反逆半群上的Clifford同余.本文中的结果是James[1],McAlister[2],Petrich[3]和Reilly[4]等人关于E-酉逆半群上的相应同余定理在E-自反逆半群上的自然推广. 相似文献
10.
11.
Cyclic subsemigroups of symmetric inverse semigroups 总被引:8,自引:0,他引:8
Stephen Leon Lipscomb 《Semigroup Forum》1986,34(1):243-248
A generalization of the cycle notation for permutations is introduced for partial one-one transformations (charts). Notational
representation theorems for charts that generalize those of permutations are given. Notational multiplication of charts is
developed and then applied to yield a transparent proof of Frobenius' result which bounds the idempotent in the cyclic subsemigroup.
Lastly, the well known result that the structure of the cyclic subgroups of the finite symmetric groups is determined from
combinations of disjoint cycles is generalized to the cyclic subsemigroups of the finite symmetric inverse semigroups. 相似文献
12.
13.
Mario Petrich 《Czechoslovak Mathematical Journal》2006,56(1):27-46
Let S be a regular semigroup and E(S) be the set of its idempotents. We call the sets S(e, f)f and eS(e, f) one-sided sandwich sets and characterize them abstractly where e, f ∈ E(S). For a, a′ ∈ S such that a = aa′a, a′ = a′aa′, we call S(a) = S(a′a, aa′) the sandwich set of a. We characterize regular semigroups S in which all S(e; f) (or all S(a)) are right zero semigroups (respectively are trivial) in several ways including weak versions of compatibility of the natural
order.
For every a ∈ S, we also define E(a) as the set of all idempotets e such that, for any congruence ϱ on S, aϱa
2 implies that aϱe. We study the restrictions on S in order that S(a) or
be trivial. For
, we define
on S by a
b if
. We establish for which S are
or
congruences. 相似文献
14.
We introduce a preorder on an inverse semigroup S associated to any normal inverse subsemigroup N, that lies between the natural partial order and Green’s \({\mathcal {J}}\)–relation. The corresponding equivalence relation \(\simeq _N\) is not necessarily a congruence on S, but the quotient set does inherit a natural ordered groupoid structure. We show that this construction permits the factorisation of any inverse semigroup homomorphism into a composition of a quotient map and a star-injective functor, and that this decomposition implies a classification of congruences on S. We give an application to the congruence and certain normal inverse subsemigroups associate to an inverse monoid presentation. 相似文献
15.
Karin Cvetko-Vah Damjana Kokol Bukovšek Tomaž Košir Ganna Kudryavtseva Yaroslav Lavrenyuk Andriy Oliynyk 《Semigroup Forum》2009,78(1):138-147
We initiate the study of semitransitive transformation semigroups. In the paper we describe the structure of semitransitive
subsemigroups of the finite symmetric inverse semigroup of the minimal cardinality modulo the classification of transitive
subgroups of the minimal cardinality of finite symmetric groups, and state the results on minimal transitive subsemigroups.
The authors were supported in part by Ukrainian-Slovenian bilateral research grants from the Ministry of Education and Science,
Ukraine, and the Research Agency of the Republic of Slovenia. 相似文献
16.
Communicated by N.R. Reilly 相似文献
18.
Let C be a regular semigroup with an inverse transversal C° and let C be generated by its idempotents. Following W. D. Munn and T. E. Hall’s idea, in this paper, a fundamental regular semigroup T C,C° with an inverse transversal T C,C° ° is constructed such that the following holds. For any regular semigroup S with an inverse transversal S° and 〈E(S)〉 = C, C° = C ∩ S°, there is a homomorphism φ from S to T C,C° such that the kernel of φ is the maximum idempotent-separating congruence on S, and φ satisfies: (1) φ| C is a homomorphism from C onto 〈E(T C,C°)〉 ; (2) φ| S° is a homomorphism from S° to T C,C° °. In particular, S is fundamental if and only if S is isomorphic to a full subsemigroup of T C,C°. Our fundamental regular semigroup T C,C° is isomorphic to a subsemigroup of the Hall semigroup of C but it is easier to handle. Its elements are partial transformations, and the operation—although not the usual composition—is defined by means of composition. 相似文献
19.
Maximal regular subsemigroups of certain semigroups of transformations 总被引:10,自引:0,他引:10
Taijie You 《Semigroup Forum》2002,64(3):391-396
Let T
n
and P
n
be the full and partial transformation semigroups on a finite set of order n respectively. The properties of the subsemigroups of T
n
and P
n
have been widely studied. But the maximal regular subsemigroups of T
n
and P
n
seem to be unknown. In this note, we determine all the maximal regular subsemigroups of all ideals of T
n
and P
n
.
April 7, 1999 相似文献
20.
We describe the structure of a regular semigroup with an associate subgroup the identiy element of which is a mcdial idempotent. As a particular application of this, we obtain the structure of perfect Dubreil-Jacotin semigroups in which the set of residuals of the bimaximum element form a subgroup. 相似文献