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1.
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
2.
V. D. Derech 《Ukrainian Mathematical Journal》2012,63(9):1390-1399
For a semigroup S, the set of all isomorphisms between the subsemigroups of the semigroup S with respect to composition is an inverse monoid denoted by PA(S) and called the monoid of local automorphisms of the semigroup S. The semigroup S is called permutable if, for any couple of congruences ρ and σ on S, we have ρ ∘ σ = σ ∘ ρ. We describe the structures of a finite commutative inverse semigroup and a finite bundle whose monoids of local automorphisms
are permutable. 相似文献
3.
Remmers (Adv. Math. 36:283–296, 1980) uses group diagrams in the Euclidean plane to demonstrate how equality in a semigroup S “mirrors” that inside the group G sharing the same presentation with S, when S satisfies Adyan’s condition—no cycles in the left/right graphs of the semigroup’s presentation. Goldstein and Teymouri (Semigroup
Forum 47:299–304, 1993) introduce a conjugacy equivalence relation for semigroups S. By closely examining the geometry of annular group diagrams in the plane, they show how their equivalence relation mirrors
conjugacy inside G, for S satisfying Adyan’s. In this article we introduce two cancellative commutative congruences. Following their leads, we examine
the geometry of group diagrams on closed surfaces of higher genera to demonstrate how these congruences mirror equality inside
two naturally associated Abelian quotient groups G/[G,G] and G/G
2, respectively. In these instances we can drop Adyan’s condition. 相似文献
4.
Ring semigroups whose subsemigroups form a chain 总被引:1,自引:1,他引:0
Greg Oman 《Semigroup Forum》2009,78(2):374-377
A multiplicative semigroup S is called a ring semigroup if an addition may be defined on S so that (S,+,⋅) is a ring. Such semigroups have been well-studied in the literature (see Bell in Words, Languages and Combinatorics,
pp. 24–31, World Scientific, Singapore, 1994; Jones in Semigroup Forum 47(1):1–6, 1993; Jones and Ligh in Semigroup Forum 17(2):163–173, 1979). In this note, we use Mihăilescu’s Theorem (formerly Catalan’s Conjecture) to characterize the ring semigroups whose subsemigroups
containing 0 form a chain with respect to set inclusion. 相似文献
5.
A semigroup is called type-E if the band of its idempotents can be expressed as a direct product of a rectangular band and an ω-chain. For brevity, we call an IC *-bisimple quasi-adequate semigroup of type-E a q
*-bisimple IC semigroup of type-E. In this paper, we characterize q
*-bisimple semigroups by using some kind of generalized Bruck-Reilly extensions. As a consequence, some results concerning
*-bisimple type-A
ω-semigroups given by Asibong-Ibe (Semigroup Forum 31:99–117, 1985) are generalized. 相似文献
6.
In this paper we give counterexamples for the open problem, posed by Blackmore (Semigroup Forum 55:359–377, 1987) of whether weak amenability of a semigroup algebra ℓ
1(S) implies complete regularity of the semigroup S. We present a neat set of conditions on a commutative semigroup (involving concepts well known to those working with semigroups,
e.g. the counterexamples are nil and 0-cancellative) which ensure that S is irregular (in fact, has no nontrivial regular subsemigroup), but ℓ
1(S) is weakly amenable. Examples are then given. 相似文献
7.
Hanson Umoh 《Semigroup Forum》1992,44(1):118-124
For α∈N with α≥2, we define and characterize α-inflatable semigroups,S and establish that the product (βS/S,·)·(βS/S,·) of Stone-Ĉech remainders does not contain the closure of the minimal ideal of (βS,·), the Stone-Ĉech compactification ofS. From this result, one can easily derive Ruppert's result that the minimal ideal of a compact left-topological semigroup
is not necessarily closed.
The author gratefully acknowledges support from Delaware State College under Grant No. 6769. 相似文献
8.
Mario Petrich 《Semigroup Forum》2005,71(3):366-388
On any regular semigroup S, the greatest idempotent pure congruence
τ the greatest idempotent separating congruence μ and the least
band congruence β are used to give the S-classification of regular semigroups as follows. These congruences generate a sublattice
Λ of the congruence lattice C(S) of S. We consider the triples (Λ,K,T), where K and T are the restrictions of the K- and T-relations
on C(S) to Λ. Such triples are characterized abstractly and form the objects of a category S whose morphisms are surjective K- and T-preserving homomorphisms subject to a mild condition. The class of regular semigroups
is made into a category S whose morphisms are fairly restricted homomorphisms. The main result of the paper is the existence of a representative functor
from S to S. The effect of the S-classification on Reilly semigroups and cryptogroups is discussed briefly. 相似文献
9.
J. C. Rosales P. A. Garcia-Sanchez J. I. Garcia-Garcia M. B. Branco 《Czechoslovak Mathematical Journal》2005,55(3):755-772
We study numerical semigroups S with the property that if m is the multiplicity of S and w(i) is the least element of S congruent with i modulo m, then 0 < w(1) < ... < w(m − 1). The set of numerical semigroups with this property and fixed multiplicity is bijective with an affine semigroup and
consequently it can be described by a finite set of parameters. Invariants like the gender, type, embedding dimension and
Frobenius number are computed for several families of this kind of numerical semigroups.
This paper was supported by the project BFM2000-1469. The fourth author wishes to acknowledge support from the Universidade
de Evora and the CIMA-UE. 相似文献
10.
Attila Nagy 《Semigroup Forum》2009,78(1):68-76
A semigroup S is said to be ℛ-commutative if, for all elements a,b∈S, there is an element x∈S
1 such that ab=bax. A semigroup S is called a generalized conditionally commutative (briefly,
-commutative) semigroup if it satisfies the identity aba
2=a
2
ba. An ℛ-commutative and
-commutative semigroup is called an
-commutative semigroup. A semigroup S is said to be a right H-semigroup if every right congruence of S is a congruence of S. In this paper we characterize the subdirectly irreducible semigroups in the class of
-commutative right H-semigroups.
Research supported by the Hungarian NFSR grant No T029525. 相似文献
11.
R. A. R. Monzo 《Semigroup Forum》2008,76(3):540-560
We determine the structure of semigroups that satisfy xyzw∈{xy,xw,zy,zw}. These semigroups are precisely those whose power semigroup is a generalised inflation of a band. The structure of generalised
inflations of the following types of semigroups is determined: the direct product of a group and a band, a completely simple
semigroup and a free semigroup F(X) on a set X. In the latter case the semigroup must be an inflation of F(X). We also prove that in any semigroup that equals its square, the power semigroup is a generalised inflation of a band if
and only if it is an inflation of a band. 相似文献
12.
A semigroup S is called a Clifford semigroup if it is completely regular and inverse. In this paper, some relations related to the least
Clifford semigroup congruences on completely regular semigroups are characterized. We give the relation between Y and ξ on completely regular semigroups and get that Y
* is contained in the least Clifford congruence on completely regular semigroups generally. Further, we consider the relation
Y
*, Y, ν and ε on completely simple semigroups and completely regular semigroups.
This work is supported by Leading Academic Discipline Project of Shanghai Normal University, Project Number: DZL803 and General
Scientific Research Project of Shanghai Normal University, No. SK200707. 相似文献
13.
Gracinda M. S. Gomes 《Acta Mathematica Hungarica》2005,109(1-2):33-51
Summary We consider proper (idempotent pure) extensions of weakly left ample semigroups. These are extensions that are injective in
each <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>\widetilde{\mathcal{R}}$-class.
A graph expansion of a weakly left ample semigroup S is shown to be such an extension of S. Using semigroupoids acted upon by weakly left ample semigroups, we prove that any weakly left ample semigroup which is a
proper extension of another such semigroup T is (2,1)-embeddable into a λ-semidirect product of a semilattice by T. Some known results, by O'Carroll, for idempotent pure extensions of inverse semigroups and, by Billhardt, for proper extensions
of left ample semigroups follow from this more general situation. 相似文献
14.
V. D. Derech 《Ukrainian Mathematical Journal》2006,58(6):836-841
A semigroup any two congruences of which commute as binary relations is called a permutable semigroup. We describe the structure
of a permutable Munn semigroup of finite rank.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 6, pp. 742–746, June, 2006. 相似文献
15.
The concepts of ℒ*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the ℒ*-inverse
semigroup can be described as the left wreath product of a type A semigroup Γ and a left regular band B together with a mapping which maps the semigroup Γ into the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups.
We shall also provide a constructed example for the ℒ*-inverse semigroups by using the left wreath products. 相似文献
16.
As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated
by El-Qallali and Fountain. As an analogy of the type W semigroups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in
on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup W
U
and a V-ample semigroup (T,V). This theorem not only generalizes a known result of Hall-Yamada for orthodox semigroups but also generalizes another known
result of El-Qallali and Fountain for type W semigroups.
This work was supported by National Natural Science Foundation of China (Grant No. 10671151) and Natural Science Foundation
of Shaanxi Province (Grant No. SJ08A06), and partially by UGC (HK) (Grant No. 2160123) 相似文献
17.
Ryszard Mazurek 《Semigroup Forum》2011,83(2):335-342
A right-chain semigroup is a semigroup whose right ideals are totally ordered by set inclusion. The main result of this paper
says that if S is a right-chain semigroup admitting a ring structure, then either S is a null semigroup with two elements or sS=S for some s∈S. Using this we give an elementary proof of Oman’s characterization of semigroups admitting a ring structure whose subsemigroups
(containing zero) form a chain. We also apply this result, along with two other results proved in this paper, to show that
no nontrivial multiplicative bounded interval semigroup on the real line ℝ admits a ring structure, obtaining the main results
of Kemprasit et al. (ScienceAsia 36: 85–88, 2010). 相似文献
18.
Brunetto Piochi 《Semigroup Forum》1991,43(1):151-162
LetS be a semigroup;S is said to bepermutable if, for some integern, every product ofn elements ofS can be re-ordered. We prove that every normal extension of a semilattice by an inverse permutable semigroupsis permutable.
Also, some properties of permutable groups are extended to inverse semigroups. 相似文献
19.
20.
Isabel M. Araújo Mário J. J. Branco Vitor H. Fernandes Gracinda M. S. Gomes N. Ruškuc 《Semigroup Forum》2001,63(1):49-62
Finite generation and presentability of general unions of semigroups, as well as of bands of semigroups, bands of monoids,
semilattices of semigroups and strong semilattices of semigroups, are investigated. For instance, it is proved that a band
Y of monoids S
α
(α∈ Y ) is finitely generated/presented if and only if Y is finite and all S
α
are finitely generated/presented. By way of contrast, an example is exhibited of a finitely generated semigroup which is
not finitely presented, but which is a disjoint union of two finitely presented subsemigroups.
January 21, 2000 相似文献