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关于左型A半群上的fuzzy同余 总被引:1,自引:0,他引:1
引入了左富足半群上fuzzy右好同余和fuzzy右消去同余的概念,给出了左富足半群上fuzzy右好同余的性质和特征.在此基础上,给出了左型A半群上fuzzy右好同余和fuzzy右消去同余的性质.得到了左型A半群上的fuzzy右好同余为fuzzy右消去同余的充要条件. 相似文献
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设ρ是半群S上的一个同余,如果S/ρ是矩形带,则称ρ是矩形同余,本文刻画了半群上的最小矩形带同余,设T是半群S的子半群,本文给出了T上每个矩形带同余能扩张成S上矩形带同余的充分必要条件。 相似文献
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本文引入了--格林关系和--富足半群,研究了满足同余条件含有中间幂等元的--富足半群.利用具有中间幂等元的由幂等元生成的正则半群和◇-拟恰当半群建立了满足同余条件含有中间幂等元的◇-富足半群的结构. 相似文献
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本文研究了一类特殊的左富足半群,即左GC-lpp-半群上的R*-同余.我们利用类似正则半群上同余的核迹方法分别刻画了这类半群上具有相同核和迹的最大和最小同余.同时,我们也得到了左GC-lpp-半群上的幂等元R*-同余的一些性质,并建立了这种同余的结构. 相似文献
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本文利用正则半群同余的概念,找到了任一强双单严格纯正半群S的一个正规子半群NK和E上的一个正规同余ГP,证明了S的任何一同余可由余偶确定,从而给出了S上任一同余的一个具体刻划。 相似文献
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Motivated by studying fuzzy congruences in groups, semigroups, and ordered semigroups, and as a continuation of N. Kuroki and Y. Tan's works in regular semigroups in terms of fuzzy subsets, in this article we introduce the notions of a fuzzy good congruence relation, a fuzzy cancellative congruence relation on abundant semigroups, and give some properties, and characterizations of fuzzy good congruences on such semigroups. Furthermore, we characterize fuzzy good congruences of left semiperfect abundant semigroups, and get sufficient and necessary conditions for an abundant semigroup to be left semiperfect. 相似文献
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介绍完全零单半群上的真模糊同余和连接模糊三元组的概念,由此得到完全零单半群上的真模糊同余集和连接模糊三元组集之间的双射。 相似文献
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带逆断面的正则半群是一类重要的正则半群.就带逆断面的正则半群类引入强模糊同余的概念,进而用所谓的强模糊同余三元组抽象地刻画带逆断面的正则半群上的强模糊同余. 相似文献
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Attila Nagy 《Semigroup Forum》2013,87(1):129-148
A semigroup S is called a left reductive semigroup if, for all elements a,b∈S, the assumption “xa=xb for all x∈S” implies a=b. A congruence α on a semigroup S is called a left reductive congruence if the factor semigroup S/α is left reductive. In this paper we deal with the left reductive congruences on semigroups. Let S be a semigroup and ? a congruence on S. Consider the sequence ? (0)?? (1)???? (n)?? of congruences on S, where ? (0)=? and, for an arbitrary non-negative integer n, ? (n+1) is defined by (a,b)∈? (n+1) if and only if (xa,xb)∈? (n) for all x∈S. We show that $\bigcup_{i=0}^{\infty}\varrho^{(i)}\subseteq \mathit{lrc}(\varrho )$ for an arbitrary congruence ? on a semigroup S, where lrc(?) denotes the least left reductive congruence on S containing ?. We focuse our attention on congruences ? on semigroups S for which the congruence $\bigcup_{i=0}^{\infty}\varrho^{(i)}$ is left reductive. We prove that, for a congruence ? on a semigroup S, $\bigcup_{i=0}^{\infty}\varrho^{(i)}$ is a left reductive congruence of S if and only if $\bigcup_{i=0}^{\infty}\iota_{(S/\varrho)}^{(i)}$ is a left reductive congruence on the factor semigroup S/? (here ι (S/?) denotes the identity relation on S/?). After proving some other results, we show that if S is a Noetherian semigroup (which means that the lattice of all congruences on S satisfies the ascending chain condition) or a semigroup in which S n =S n+1 is satisfied for some positive integer n then the universal relation on S is the only left reductive congruence on S if and only if S is an ideal extension of a left zero semigroup by a nilpotent semigroup. In particular, S is a commutative Noetherian semigroup in which the universal relation on S is the only left reductive congruence on S if and only if S is a finite commutative nilpotent semigroup. 相似文献
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In this paper we study the congruences of *-regular semigroups, involution semigroups in which every element is p-related
to a projection (an idempotent fixed by the involution). The class of *-regular semigroups was introduced by Drazin in 1979,
as the involutorial counterpart of regular semigroups. In the standard approach to *-regular semigroup congruences, one ,starts
with idempotents, i.e. with traces and kernels in the underlying regular semigroup, builds congruences of that semigroup,
and filters those congruences which preserve the involution. Our approach, however, is more evenhanded with respect to the
fundamental operations of *-regular semigroups. We show that idempotents can be replaced by projections when one passes from
regular to *-regular semigroup congruences. Following the trace-kernel balanced view of Pastijn and Petrich, we prove that
an appropriate equivalence on the set of projections (the *-trace) and the set of all elements equivalent to projections (the
*-kernel) fully suffice to reconstruct an (involution-preserving) congruence of a *-regular semigroup. Also, we obtain some
conclusions about the lattice of congruences of a *-regular semigroup.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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《代数通讯》2013,41(6):2061-2085
Abstract The aim of this paper is to study some special lpp-semigroups, namely, the left GC-lpp semigroups. After obtaining some properties and characterizations of such semigroups, we establish some structure theorems of this class of semigroups. In addition, we also consider some special cases. As an application, we describe the structure theorems of IC quasi-adequate semigroups whose idempotent band is a regular band. 相似文献