共查询到20条相似文献,搜索用时 15 毫秒
1.
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
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The main result of the paper is a decomposition theorem of the left regular ordered semigroups into left regular and left simple semigroups. 相似文献
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A new class of semigroups with a two variable regularity law is introduced. These semigroups are non-regular semigroups but they are closely related to regular semigroups. The local and global structures of this class of semigroups are investigated.AMS Subject Classification (2000): 20M10Partially supported by a Chinese University of Hong Kong Direct Research grant, Hong Kong (98/99) # 2060152.Partially supported by a grant of the National Science Foundation, China. 相似文献
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完全单半群及完全正则半群的逆断面 总被引:1,自引:1,他引:0
指出完全单半群S的任何一个F-类是逆断面,且为Q-逆断面,而S的任何一个逆断面必是一个F-类,因而所有逆断面同构。并且给出完全正则半群的逆断面存在的充要条件。 相似文献
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本文先证明了正则orthocryptou半群关于矩形单幂幺半群的加细半格分解是唯一的,在此基础上,给出了任意两个正则orthocryptou半群之间好同态的刻画. 相似文献
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设A是代数闭域k上的一个具乘基B的有限维含幺结合代数,称半群B∪{0}为A的基半群.本文给出了0 J 严格单半群的定义.对于基半群为0 J 严格单半群的零直并的代数,完全研究了它的代数表示型 相似文献
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本文研究了完全正则半群簇的子簇格[V+∩PV,V+∩PV]的某些格运算性质,我们证明了簇V+∩PV可分解为V与V+∩PV的并;对任意完全正则半群簇W,有W∩(V∨V+∩PV)=(W∩V)∨(W∩V+∩PV).特别地,我们得到了等式V+∩PV=V成立的若干条件. 相似文献
10.
Mario Petrich 《代数通讯》2013,41(4):1397-1413
In a previous communication, we defined a countably infinite sequence of varieties of completely regular semigroups, termed canonical. Finite intersections of these varieties constitute the upper ends of the intervals which are the classes of the congruence induced by the complete homomorphism 𝒱 → 𝒱 ∩ ?, where ? is the variety of all bands. We construct here the lattice generated by the first few of these varieties in some detail. In particular, we determine their bases and illustrate our findings by three diagrams. 相似文献
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Edmond W. H. Lee 《代数通讯》2013,41(1):323-334
Let R be a ring regarded as a multiplicative semigroup which contains no infinite subsemilattices. We investigate subsemigroups of R which are normal orthogroups, and present a construction from which all such maximal normal orthogroups can be obtained. In particular, we construct all maximal normal orthogroups of matrices over a field under matrix multiplication. Communicated by D. Easdown. 相似文献
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设S是一个正则半群,如果存在一个S的子半群S~*及上的一元运算*满足条件:(1)(?)x∈S,x~*∈S~*∩V(x);(2)(?)x∈S~*,(x~*)~*=x;(3)(?)x,y∈S,(x~*y)~*=y~*x~(**),(xy~*)~*=y~(xx)x~*则称S~*是S的一个正则*_-断面.本文刻画了具有正则*_-断面的正则半群的结构。 相似文献
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本文分别讨论了关于结合环和半群的二个定理,并且由结合环的这二个定理推出了如下准则:结合环R是Abel正则的,当且仅当R的每个拟理想是正则环. 相似文献
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P. G. Trotter 《代数通讯》2013,41(8):2920-2932
For any semigroup S a regular semigroup 𝒞(S) that embeds S can be constructed as the direct limit of a sequence of semigroups each of which contains a copy of its predecessor as a subsemigroup whose elements are regular. The construction is modified here to obtain an embedding of S into a regular semigroup R such that the nontrivial maximal subgroups of R are isomorphic to the Schützenberger groups of S and such that the restriction to S of any of Green's relations on R is the corresponding Green's relation on S. 相似文献
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具有拟理想正则*-断面的正则半群 总被引:4,自引:1,他引:3
本文提出了具有正则*-断面正则半群的概念,所给出的例子表明具有拟理想正则*-断面的正则半群类真包含了具有拟理想逆断面的正则半群类和正则*-半群类;最后刻画了具有拟理想正则*-断面的正则半群的结构. 相似文献
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本文给出了带正则*-断面的正则半群的若干性质,获得了带拟理想正则*-断面的正则半群的一个构造方法.利用这一构造定理,考虑了这类半群上的同余. 相似文献
19.
Yupaporn Kemprasit 《Southeast Asian Bulletin of Mathematics》2002,25(4):617-622
Let V and W be vector spaces over a division ring D and LD (V, W) the set of all linear transformations from V into W. For LD(W, V), let (LD (V, W), ) denote the semigroup LD (V, W) with the operation * defined by * = for all , LD(V, W). By a unit-regular semigroup we mean a semigroup S with identity having the property that for each a S, a = aua for some unit u S. The main purpose of this paper is to prove the following statements. The semigroup (LD(V, W), ) is regular if and only if V = {0}, W = {0} or is an isomorphism from W onto V. The semigroup (LD (V, W), ) is unit-regular if and only if (i) V = {0}, (ii) W = {0} or (iii) is an isomorphism from W onto V and dimD V . 相似文献
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N. D. Gilbert 《Applied Categorical Structures》2003,11(2):147-155
We study the structure of the flow monoid of a regular semigroup. This arises from the approach of Nambooripad of considering a regular semigroup as a groupoid – a category in which every morphism is invertible. A flow is then a section to the source map in this groupoid, and the monoid structure of the set of all flows is determined in terms of the Green relations on the original semigroup. 相似文献