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1.
一类阿基米德半群的构造及其同余格   总被引:4,自引:0,他引:4  
朱聘瑜 《数学学报》1993,36(3):392-396
本文引入同底的π-左、右零半群的夹群积并用来刻划带本原幂等元的阿基米德半群的构造.文中讨论了有限阶阿基米德半群的同余格,并证明了当有限阶阿基米德半群的正则R,L类的个数不超过5时,它的同余格是半模格.  相似文献   

2.
朱聘瑜 《数学季刊》1990,5(4):54-59
半群的代数理论的一个重要课题是研究半群S的同余的特性对于S的结构的影响。作为这个课题的一个方面是研究同余可交换半群的性质。本文借助有限R-平凡半群构造定理[5]来研究有限R-平凡的同余可交换半群的分类。设S是半群。S的同余格记为C(S)。设x∈S,ρ∈C(s),x所在的ρ-类记为xρ。S称为同余可交换半群(简称为P-半群),如果ρ°σ=σ°ρ  相似文献   

3.
利用半群fuzzy同余的概念,讨论一类特殊的完全正则半群,即Clifford半群上的fuzzy同余.研究该类半群上fuzzy同余的性质.在此基础上,给出Clifford半群上fuzzy同余的性质和特征,得到Cllifford半群上fuzzy同余为fuzzy消去同余的充要条件.  相似文献   

4.
序半群S的什么子集可以作为S的同余类是一个重要的问题. 在文[8]中,作者证明了如果序半群S的 理想$C$是$S$的某个同余类, 则$C$是凸的; 而且当$C$是强凸理想时,逆命题成立. 在本文中, 我们给出了序半群同余的一个新的构造,并证明了序半群$S$的理想$B$是$S$的某个同余类的充要条件是$B$是凸的.  相似文献   

5.
朱凤林  宋光天 《数学杂志》2004,24(6):595-600
左半正规纯正半群是幂等元集形成左半正规带的纯正半群.本文讨论了具有逆断面的左半正规纯正半群上的一些性质;给出该类半群的一个构造定理。  相似文献   

6.
朱雯  何明星 《数学杂志》1999,19(4):411-415
本文讨论G逆半群上的同余,文中给出刻划p^k,pk,p^T,pT的方法,并用来讨论半格同余,纯幂同余,群同余及幂等元分离同余。  相似文献   

7.
关于G逆半群的构造   总被引:1,自引:1,他引:0  
朱雯 《数学杂志》1999,19(3):282-286
本文讨论一类重要的半群即G逆半群,文中给出G逆半群的主要的几例子,并详尽地讨论了G逆半群的构造。  相似文献   

8.
研究了幺半群半直积上的同余,给出了幺半群半直积的所谓同余分解定理,并特别讨论了幺半群左正则纯整半直积及其子类上的同余.  相似文献   

9.
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   

10.
本文证明了有限幂零半群的构造定理并用来研究有限幂零半群的同余格,给出有限幂零半群的同余格是模格的必要条件。对于齐次的有限幂零半群还证明了该条件是充分的。  相似文献   

11.
曹永林 《数学杂志》1999,19(2):161-166
作为拟C-半群的推广,本文定义了左半正则纯整群并群,给出了它的左半织积结构。讨论了两类特殊的右(右)半正则纯整群并半群,得出了左(右)半正则纯整群并半群类与拟C-半群类之间的关系。  相似文献   

12.
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   

13.
A new kind of regular orthogroups, namely, the LR-normal orthogroups is introduced and investigated. In particular, we will introduce the gearing techniques for fitting semigroup components on a semilattice in the construction of LR-normal orthogroups.  相似文献   

14.
A new kind of regular orthogroups, namely, the LR-normal orthogroups is introduced and investigated. In particular, we will introduce the gearing techniques for fitting semigroup components on a semilattice in the construction of LR-normal orthogroups.  相似文献   

15.
Congruence Permutable Symmetric Extended de Morgan Algebras   总被引:1,自引:0,他引:1  
An algebra A is said to be congruence permutable if any two congruences on it are permutable. This property has been investigated in several varieties of algebras, for example, de Morgan algebras, p-algebras, Kn,0-algebras. In this paper, we study the class of symmetric extended de Morgan algebras that are congruence permutable. In particular we consider the case where A is finite, and show that A is congruence permutable if and only if it is isomorphic to a direct product of finitely many simple algebras.  相似文献   

16.
The aim of this paper is to prove certain characterization theorems for groups in which permutability is a transitive relation, the so called -groups. In particular, it is shown that the finite solvable -groups, the finite solvable groups in which every subnormal subgroup of defect two is permutable, the finite solvable groups in which every normal subgroup is permutable sensitive, and the finite solvable groups in which conjugate-permutability and permutability coincide are all one and the same class. This follows from our main result which says that the finite modular p-groups, p a prime, are those p-groups in which every subnormal subgroup of defect two is permutable or, equivalently, in which every normal subgroup is permutable sensitive. However, there exist finite insolvable groups which are not -groups but all subnormal subgroups of defect two are permutable. Received: 13 August 2008  相似文献   

17.
A. Van Daele 《代数通讯》2013,41(6):2341-2386
A simple and nice structure theorem for orthogroups was given by Petrich in 1987. In this paper, we consider a generalized orthogroup, that is, a quasi-completely regular semigroup with a band of idempotents in which its set of regular elements, namely, RegS, forms an ideal of S. A method of construction of such semigroups is provided and as a result, the Petrich structure theorem of orthogroups becomes an immediate corollary of our theorem on generalized orthogroups. An example of such generalized orthogroup is also constructed. This example provides some useful information for the construction of various kinds of quasi-completely regular semigroups.  相似文献   

18.
A new kind of regular orthogroups, namely, the LR-normal orthogroups is introduced and investigated. In particular, we will introduce the gearing techniques for fitting semigroup components on a semilattice in the construction of LR-normal orthogroups.  相似文献   

19.
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   

20.
We characterize orthogroups, local orthogroups and (left,right) cryptogroups within completely regular semigroups by means of absence of certain kind of subsemigroups. For each of these varieties V, we determine the complete set of minimal non-V -varieties. For each of the latter varieties, we determine the lattice of its subvarieties. We then give a generating semigroup and a basis of its identities for every variety which occurs in this way. The subvariety lattices are illustrated by three diagrams.  相似文献   

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