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1.
A left GC-lpp semigroup S is called split if the natural homomorphism γb of S onto S/γ induced by γ is split.It is proved that a left GC-lpp semigroup is split if and only if it has a left adequate transversal.In particular,a construction theorem for split left GC-lpp semigroups is established. 相似文献
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设S,R是可分解半群.记US-FAct={sM∈S-Act|SM=M且SHoms(S,M)≌M],给出了范畴US-FAct与UR-FAct等价的刻划;S分别强Morita等价于一个夹层半群、局部单位半群、幺半群和群的条件;S是完全单半群当且仅当S强Morita等价于一个群且对任何指标集I,S SHoms(S,i∈I S)→i∈I S,s t·f→(st)f,是同构. 相似文献
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本文通过一个序半群S上的一些二元关系以及它的理想(右理想,双理想)的根集分别给出了该序半群是阿基米德(右阿基米德,t-阿基米德)序子半群的链的刻画.进一步证明了准素序半群是阿基米德序半群的链.最后,通过素根定理证明了序半群S是阿基米德序子半群的链当且仅当S是阿基米德序子半群的半格且S的所有素理想关于集合的包含关系构成链. 相似文献
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The so-called split IC quasi-adequate semigroups are in the class of idempotent-connected quasi-adequate semigroups. It is
proved that an IC quasi-adequate semigroup is split if and only if it has an adequate transversal. The structure of such semigroup
whose band of idempotents is regular will be particularly investigated. Our obtained results enrich those results given by
McAlister and Blyth on split orthodox semigroups. 相似文献
5.
We characterize the ordered semigroups which are decomposable into simple and regular components. We prove that each ordered semigroup which is both regular and intra-regular is decomposable into simple and regular semigroups, and the converse statement also holds. We also prove that an ordered semigroup S is both regular and intra-regular if and only if every bi-ideal of S is an intra-regular (resp. semisimple) subsemigroup of S. An ordered semigroup S is both regular and intra-regular if and only if the left (resp. right) ideals of S are right (resp. left) quasi-regular subsemigroups of S. We characterize the chains of simple and regular semigroups, and we prove that S is a complete semilattice of simple and regular semigroups if and only if S is a semilattice of simple and regular semigroups. While a semigroup which is both π-regular and intra-regular is a semilattice of simple and regular semigroups, this does not hold in ordered semigroups, in general. 相似文献
6.
The main result of the paper is a structure theorem concerning the ideal extensions of archimedean ordered semigroups. We
prove that an archimedean ordered semigroup which contains an idempotent is an ideal extension of a simple ordered semigroup
containing an idempotent by a nil ordered semigroup. Conversely, if an ordered semigroup S is an ideal extension of a simple ordered semigroup by a nil ordered semigroup, then S is archimedean. As a consequence, an ordered semigroup is archimedean and contains an idempotent if and only if it is an
ideal extension of a simple ordered semigroup containing an idempotent by a nil ordered semigroup. 相似文献
7.
本文研究了左$C$-wrpp半群的加细半格结构,证明了左$C$-wrpp半群是左-${\cal R}$可消带的加细半格当且仅当它是一个$C$-wrpp半群和一个左正则带的织积. 相似文献
8.
A left GC-lpp semigroup S is called split if the natural homomorphism γb of S onto S/γ induced by γ is split.It is proved that a left GC-lpp semigroup is split if and only if it has a left adequate transversal.In particular,a construction theorem for split left GC-lpp semigroups is established. 相似文献
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Free completely <Emphasis Type="Italic">J</Emphasis><Superscript>(<Emphasis Type="Italic">ℓ</Emphasis>)</Superscript>-simple Semigroups 下载免费PDF全文
A semigroup is called completely J(ι)-simple if it is isomorphic to some Rees matrix semigroup over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid. It is proved that completely J(ι)-simple semigroups form a quasivarity. Moreover, the construction of free completely J(ι)-simple semigroups is given. It is found that a free completely J(ι)-simple semigroup is just a free completely J *-simple semigroup and also a full subsemigroup of some completely simple semigroups. 相似文献
11.
具有理想收缩性质的某些GV-半群(英文) 总被引:1,自引:0,他引:1
如果半群S的每一个理想都是它的幂等同态像,称半群S具有理想收缩性质。GV-半群是完全正则半群在π-正则半群范围内的推广。本文刻画了某些具有理想收缩性质的GV-半群。 相似文献
12.
高德智 《应用泛函分析学报》2001,3(4):294-299
一个n次积分半群S(t)如果满足‖S^(n)(t)x‖≤‖x‖,A↓t≥0,x∈D(A^n),我们就称S(t)是一压缩的n次积分半群,其中A为半群S(t)的生成元。在本中,我们完全刻划了n次压缩积分半群的特征,给出了n次压缩积分半群的Lumer-Phillips定理。 相似文献
13.
Alexei Vernitski 《Semigroup Forum》2009,78(3):486-497
We prove a number of results related to finite semigroups and their inverse subsemigroups, including the following. (1) A finite
semigroup is aperiodic if and only if it is a homomorphic image of a finite semigroup whose inverse subsemigroups are semilattices.
(2) A finite inverse semigroup can be represented by order-preserving mappings on a chain if and only if it is a semilattice.
Finally, we introduce the concept of pseudo-small quasivariety of finite semigroups, generalizing the concept of small variety. 相似文献
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Ernie Manes 《Semigroup Forum》2006,72(1):94-120
The variety of guarded semigroups consists of all (S,·, ˉ) where (S,·) is a semigroup and x ↦ \overline{x} is a unary operation
subject to four additional equations relating it to multiplication. The semigroup Pfn(X) of all partial transformations on
X is a guarded semigroup if x \overline{f} = x when xf is defined and is undefined otherwise. Every guarded semigroup is
a subalgebra of Pfn(X) for some X. A covering theorem of McAlister type is obtained. Free guarded semigroups are constructed
paralleling Scheiblich's construction of free inverse semigroups. The variety of banded semigroups has the same signature
but different equations. There is a canonical forgetful functor from guarded semigroups to banded semigroups. A semigroup
underlies a banded semigroup if and only if it is a split strong semilattice of right zero semigroups. Each banded semigroup
S contains a canonical subsemilattice g⋆(S). For any given semilattice L, a construction to synthesize the general banded semigroup S with g⋆ ≅ L is obtained. 相似文献
16.
SHUM K.P. 《中国科学 数学(英文版)》2010,(4)
A U-abundant semigroup S in which every H-class of S contains an element in the set of projections U of S is said to be a U-superabundant semigroup.This is an analogue of regular semigroups which are unions of groups and an analogue of abundant semigroups which are superabundant.In 1941,Clifford proved that a semigroup is a union of groups if and only if it is a semilattice of completely simple semigroups.Several years later,Fountain generalized this result to the class of superabundant semigroups.In this p... 相似文献
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Orthodox semigroups whose idempotents satisfy a certain identity 总被引:2,自引:0,他引:2
Miyuki Yamada 《Semigroup Forum》1973,6(1):113-128
An orthodox semigroup S is called a left [right] inverse semigroup if the set of idempotents of S satisfies the identity xyx=xy
[xyx=yx]. Bisimple left [right] inverse semigroups have been studied by Venkatesan [6]. In this paper, we clarify the structure
of general left [right] inverse semigroups. Further, we also investigate the structure of orthodox semigroups whose idempotents
satisfy the identity xyxzx=xyzx. In particular, it is shown that the set of idempotents of an orthodox semigroup S satisfies
xyxzx=xyzx if and only if S is isomorphic to a subdirect product of a left inverse semigroup and a right inverse semigroup. 相似文献
19.
If S is a semigroup, the global (or the power semigroup) of S is the set P(S) of all nonempty subsets of S equipped with a naturally defined multiplication. A class K of semigroups is globally determined if any two semigroups of K with isomorphic globals are themselves isomorphic. We study properties of globals of idempotent semigroups and show, in particular, that the class of normal bands is globally determined. 相似文献
20.
本文研究有Clifford断面的纯正半群.为了获得主要的结构定理,证明了纯正半群有群断面当且仅当它是矩形群;利用半格和矩形带,建立了有Clifford断面的纯正半群的结构. 相似文献