共查询到20条相似文献,搜索用时 93 毫秒
1.
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
2.
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
3.
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
4.
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
5.
关于同余交换纯正群并的构造与分类 总被引:4,自引:0,他引:4
本文讨论同余交换纯正群并的构造与分类。文中将该类半群给出分解方法,指出该类半群是它的左,右分量的织积。接着给出该类半群的完整分类,指出共有20类并给出各类的构造,上述结论还用来讨论同余交换带,文中给出所有29个同余交换带的构造并证明同余交换带都是有限的且元素个数不超过13. 相似文献
6.
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
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8.
Mario Petrich 《Semigroup Forum》2003,66(3):381-400
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
9.
Mario Petrich 《Semigroup Forum》2008,66(3):381-400
Abstract. 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
10.
11.
M. Petrich 《Acta Mathematica Hungarica》2009,125(1-2):1-15
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刻画半群上的同余及其扩张是半群的代数理论中的一个非常重要的课题(参见[1-5])本文在[6]讨论了带上的同余的正规性和不变性以及在其Hall半群上的扩张的基础上,从同余扩张的角度刻划了完全正则的纯正半群的特征(定理26),给出了一个纯正半群的带上的所有同余都可以扩张到这个纯正半群的充分必要条件. 相似文献
14.
If S is a semigroup, the global (or the power semigroup) of S is the set \(\mathcal {P}(S)\) of all nonempty subsets of S equipped with the naturally defined multiplication. A class \(\mathcal {K}\) of semigroups is globally determined if any two semigroups of \({\mathcal {K}}\) with isomorphic globals are themselves isomorphic. We study properties of globals of normal orthogroups and show, in particular, that the class of normal orthogroups is globally determined. 相似文献
15.
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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We shall show that a completely regular semigroup is in the semigroup variety generated by the bicyclic semigroup if and only if it is an orthogroup whose maximal subgroups are abelian. Therefore the lattice of subvarieties of the variety generated by the bicyclic semigroup contains as a sublattice a countably infinite distributive lattice of semigroup varieties, each of which consists of orthogroups with maximal subgroups that are torsion abelian groups. In particular, every band divides a power of the bicyclic semigroup.Presented by B. M. Schein. 相似文献
18.
In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E(S)-semiabundant semigroups. After introducing the concept of (∼)-Green’s relations, and obtaining some important properties
of (∼)-Green’s relations and super E(S)-semiabundant semigroups, we have given the semilattice decomposition of ortho-u-monoids and a structure theorem for regular
ortho-u-monoids. The main techniques that we used in the study are the (∼)-Green’s relations, and the semi-spined product
of semigroups. 相似文献
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20.
A regular orthogroup S with the property that D
e
=R
e
or D
e
=L
e
for any idempotent e∈S is called a WLR-regular orthogroup. In this paper, we give constructions of such semigroups in terms of spined products of
left and right regular orthogroups with respect to Clifford semigroups. WLR-cryptogroups and its special cases are also investigated.
Research supported by General Scientific Research Project of Shanghai Normal University No. SK200707. 相似文献