共查询到20条相似文献,搜索用时 109 毫秒
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给出了两个半群S和T的半直积是Clifford拟正则半群的充要条件,同时还讨论了S和T^e半直积的结构,其中T^e={t^e|Vt∈T,Vc∈E(S)}。 相似文献
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给出了纯正半群S的强同余格上同余T的一些判别性质,证明了S上所有基础强同余所构成的集合FCP(S)是CP(S)的完备子格,最后讨论了由纯正半群的正规子半群决定的交完备子格的结构及由“求核”运算确定的(交完备格)同余K的若干性质,还顺带讨论了群同余格. 相似文献
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研究了加法半群为半格,乘法半群为左正规纯正群的半环.证明了此类半环(S,+,.)可以嵌入到半格(S,+)的自同态半环中.构造S的一个特定的偏序关系,得到了(S,·)上的自然偏序与所构造偏序相等的等价条件. 相似文献
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强P-正则半群上的最小正则*-半群同余 总被引:2,自引:2,他引:0
陈迪三 《纯粹数学与应用数学》2009,25(1):142-144
主要研究了强P-正则半群S(P)上的最小正则*-半群同余.利用S(P)的正则*-断面S°得到S(P)上最小正则*-半群同余的简单形式γP.由于S(P)/γP同构于S°,实质上S°是S(P)的最大正则*-半群同态象,且S(P)的正则*-断面不唯一,但从同意义上看正则*-断面唯一. 相似文献
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引入了0-恰当半群的概念,它是一种特殊的逆半群.给出了0-恰当半群的等价刻划.讨论具有幂等半格的右0-恰当半群上含于(够)0的最大同余关系μL和具有幂等半格的0-恰当半群上含于(形)0的最大同余关系μ.证明如果S是一个具有幂等半格E的右0-A型半群,则S/μL≌E当且仅当S是一个S0左逆的左消含幺半群的强半格.进一步证明了,如果S是一个具有幂等半格E的0-恰当半群,则S/μ≌E当且仅当S是一个S0逆的消去含幺半群的强半格. 相似文献
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阿贝尔群的完整子半群的若干结果 总被引:3,自引:0,他引:3
本文证明了无扭阿贝尔群G是唯一线性序的,当且仅当G的每一个完整子半群只含唯一的极小完整子半群。若群G的每一个完整子半群只含有限多个极小完整子半群,则G中所有完整子半群组成的集T(G)满足DCC。 相似文献
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It is shown that each regular congruence on an eventually regular semigroup is uniquely determined by its kernel and hyper-trace.
Furthermore, the orthodox congruences (resp., the
regular congruences ) on an eventually regular (resp., orthodox) semigroup S are described by means of certain congruence
pair (ξ, K), where ξ is a certain normal congruence on the subsemigroup 〈E(S)〉 generated by E(S) and K is a certain normal
subsemigroup of S. 相似文献
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Guangtian Song 《Semigroup Forum》1995,51(1):295-298
LetR be a ring with identity,S be a semigroup with the set of idempotentsE(S), and denote (E(S)) for the subsemigroup ofS generated byE(S). In this paper, we prove that ifS is a semilattice of completely 0-simple semigroups and completely simple semigroups, then the semigroup ringRS possesses an identity iff so doesR(E(S)); especially, the result is true forS being a completely regular semigroup. 相似文献
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G. Lallement [5] proved that every idem potent congruence class of a regular semigroup contains an idem potent. P. Edwards [4] generalized this property of congruences to eventually regular semigroups. Using the natural partial order of the semigroup (see [6]) a weakened version of this result will be proved for the more general class of E-inversive semigroups. But for particular congruences the original result of Lallement still holds for every E-inversive semigroup. Finally, conditions for a congruence on a general semigroup (with E(S) a subsemigroup, resp.) are given, which ensure that Lallement's result holds. 相似文献
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Melanija Mitrovic 《Semigroup Forum》2005,70(3):356-360
For a subsemigroup T of a semigroup S, we let Reg(T)
and reg(T) denote respectively the set of all regular elements of T
and the set of all elements of T which are regular in S. We characterize
semigroups with Reg(T)=reg(T), where T runs over one of the following
families of subsemigroups: {Se | e ∈ E(S)}, {eS | e ∈ E(S)},
{eSf | e,f ∈ E(S)}. 相似文献
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Regular four-spiral semigroups,idempotent-generated semigroups and the rees construction 总被引:1,自引:0,他引:1
Karl Byleen 《Semigroup Forum》1981,22(1):97-100
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含幺Clifford半群上的Rees矩阵半群的同余和正规加密群结构 总被引:1,自引:0,他引:1
给出了含幺Clifford半群上的Rees矩阵半群S的正规加密群结构,证明了在含幺Clifford半群上的Rees矩阵半群S上以下两个条件是等价的:(1)S上的同余ρ是完全单半群同余;(2)S上的同余ρ和S上的相容组之间存在保序双射.最后还证明了S上的完全单半群同余所构成的同余格是半模的. 相似文献
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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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Let S be a regular semigroup with set of idempotents E(S) . Given x,y ∈ S , we say that (x,y) is a skew pair if x y \notin E(S) whereas y x ∈ E(S) . Here we use this concept to characterise certain regular Rees matrix semigroups. 相似文献
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Francis T. Christoph Jr. 《Semigroup Forum》1970,1(1):224-231
In [6] Rothman investigated the problem of embedding a topological semigroup in a topological group. He defined a concept
calledProperty F and showed that Property F is a necessary and sufficient condition for embedding a commutative, cancellative topological
semigroup in its group of quotients as an open subset. This paper announces a generalization of Rothman’s result by definingProperty E and stating that a completely regular topological semigroup S can be embedded in a topological group by a topological isomorphism
if and only if S can be embedded (algebraically) in a group and S has Property E. Property E is defined by first constructing
a free topological semigroup (Theorem 1.1). This construction resembles the one in [4] for a free topological group. Full
details, examples, and other embedding results will appear elsewhere.
Some of the results in this paper were contained in the author’s doctoral dissertation written at Rutgers University under
Professor Louis F. McAuley. 相似文献
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Let S be a countably compact Hausdorff space endowed with a continuous
semigroup operation turning S into an inverse semigroup. It is shown that
the inversion inv : x x-1 in S is continuous provided one of the following
conditions is satisfied: (1) the space S is sequential, (2) the semigroup S is
Clifford, inversely regular, and topologically periodic, (3) the semigroup S is
Clifford, topologically periodic and the square S × S is regular and countably
compact. These results are close to the best possible since there is an example of
a quasi-regular sequentially compact commutative inverse topological semigroup
with discontinuous inversion. 相似文献