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1.
Karin Cvetko-Vah 《Semigroup Forum》2005,71(1):93-101
Jonathan Leech proved in [8] that the multiplicative reduct of a
skew lattice in a ring is always a regular band. A band that is
closed under the operation ∇ is called a ∇-band. A
∇-band is also always regular. We show that a regular band does
not generate a ∇-band in general, but does so in the
special case of regular pure bands. An exact condition for a pure
∇-band to form a skew lattice was found in [1]. 相似文献
2.
本文研究了正则带的结构问题.利用拟强半格分解方法,获得了带为正则带当且仅当它为矩形带的拟强半格,推广了Yamada和Kimura关于正规带是矩形带的强半格的结果. 相似文献
3.
On the structure of semigroups of idempotent matrices 总被引:1,自引:0,他引:1
Karin Cvetko-Vah 《Linear algebra and its applications》2007,426(1):204-213
We prove that any pure regular band of matrices admits a simultaneous LU decomposition in the standard form. In case that such a band forms a double band called a skew lattice, we obtain the standard form without the assumption of purity. 相似文献
4.
Bands in lattices of operators 总被引:1,自引:0,他引:1
C. B. Huijsmans A. W. Wickstead 《Proceedings of the American Mathematical Society》1996,124(12):3835-3841
We consider the lattice of regular operators on a Dedekind complete Banach lattice. We show that in general the projection onto a band generated by a lattice homomorphism need not be continuous and that the principal bands need not be closed for the operator norm. In fact it is possible to find a convergent sequence of operators all the members of which are disjoint from the limit.
5.
Roman S. Gigoń 《代数通讯》2017,45(7):3045-3051
We show that an exponential epigroup is a band of unipotent exponential epigroups (in which the set of idempotents forms a subsemigroup). Also, we investigate the structure of unipotent exponential epigroups. In addition, a characterization of the least normal band of groups congruence is given for an arbitrary medial epigroup. It is also shown that k-exponential eventually regular semigroups are necessarily epigroups. 相似文献
6.
Varieties of idempotent semirings with commutative addition 总被引:3,自引:0,他引:3
The multiplicative reduct of an idempotent semiring with commutative addition is a regular band. Accordingly there are 13
distinct varieties consisting of idempotent semirings with commutative addition corresponding to the 13 subvarieties of the
variety of regular bands. The lattice generated by the these 13 semiring varieties is described and models for the semirings
free in these varieties are given.
Received April 22, 2004; accepted in final form June 3, 2005. 相似文献
7.
Positivity - We consider the structure of the lattice of (order and algebra) ideals of the band of regular kernel operators on $$L^p$$ -spaces. We show, in particular, that for any $$L^p(\mu )$$... 相似文献
8.
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
9.
The lattice of idempotent distributive semiring varieties 总被引:7,自引:0,他引:7
A solution is given for the word problem for free idempotent distributive semirings. Using this solution the latticeL (ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns out thatL (ID) is isomorphic to the direct product of a four-element lattice and a lattice which is itself a subdirect product of four
copies of the latticeL(B) of all band varieties. ThereforeL(ID) is countably infinite and distributive. Every subvariety of ID is finitely based.
Project supported by the National Natural Science Foundation of China (Grant No. 19761004) and the Provincial Applied Fundamental
Research Foundation of Yunnan (96a001z). 相似文献
10.
11.
ABSTRACT The investigation of regular F-abundant semigroups is initiated. In fact, F-abundant semigroups are generalizations of regular cryptogroups in the class of abundant semigroups. After obtaining some properties of such semigroups, the construction theorem of the class of regular F-abundant semigroups is obtained. In addition, we also prove that a regular F-abundant semigroup is embeddable into a semidirect product of a regular band by a cancellative monoid. Our result is an analogue of that of Gomes and Gould on weakly ample semigroups, and also extends an earlier result of O'Carroll on F-inverse semigroups. 相似文献
12.
We study another structure of so-called left C-wrpp semigroups. In particular, the concept of left △-product is extended and enriched. The aim of this paper is to give a construction of left C-wrpp semigroups by a left regular band and a strong semilattice of left-R cancellative monoids. Properties of left C-wrpp semigroups endowed with left △-products are particularly investigated. 相似文献
13.
Raymond Broeksteeg 《Semigroup Forum》1994,49(1):335-348
We define a bivariety of regular biordered sets to be a nonempty class of regular biordered sets which is closed under taking
direct products, regular bimorphic images and relatively regular biordered subsets. It is then shown that there is a complete
lattice morphism mapping the complete lattice of all e-varieties of regular semigroups onto the complete lattice of all bivarieties
of regular biordered sets; as a corollary we prove that there is a complete lattice morphism mapping the complete lattice
of all e-varieties of E-solid regular semigroups onto the complete lattice of all varieties of solid binary algebras. Examples
of bivarieties include the class of all solid regular biordered sets and the class of all local semilattices. For each setX with at least two elements, we show that a bivariety contains a free object onX if and only if it consists entirely of solid regular biordered sets or it consists entirely of local semilattices.
The author gratefully acknowledges the financial support of an Australian Postgraduate Research Award. 相似文献
14.
Igor Dolinka 《代数通讯》2013,41(6):2837-2852
In the present paper, we study varieties consisting of bands (idempotent semigroups) endowed with an involutorial antiautomorphism * as a fundamental operation. Our principal aim is here to provide an insight to some classes of these varieties from the structural point of view, especially in terms of semilattice decompositions, subdirect products and ideal extensions. In the course of such considerations, we shall extend the result of C. L. Adair [1], who described the lattice of all varieties of bands with a regular involution (i.e. with the identity x = xx * x) We depict a broader lattice of involution band varieties, which incorporates Adair’s lattice. 相似文献
15.
16.
明平华 《数学物理学报(A辑)》2004,24(4):491-495
该文在文[1]中幂格概念的基础上,得到了幂格的一个充要条件,给出了正则幂格、相对幂格的概念,并讨论了商格与正则幂格、相对幂格的关系.〖HT5”H〗关键词:〖HT5”SS〗格;幂格;商格;正则幂格;相对幂格. 相似文献
17.
The so-called split IC quasi-adequate semigroups are in the class of idempotent-connected quasi-adequate semigroups. It is
proved that an IC quasi-adequate semigroup is split if and only if it has an adequate transversal. The structure of such semigroup
whose band of idempotents is regular will be particularly investigated. Our obtained results enrich those results given by
McAlister and Blyth on split orthodox semigroups. 相似文献
18.
Pseudovarieties of completely regular semigroups 总被引:1,自引:0,他引:1
Francis Pastijn 《Semigroup Forum》1991,42(1):1-46
19.
20.
Z. J. Tian 《Vestnik St. Petersburg University: Mathematics》2007,40(2):152-157
It is shown that all regular subsemigroups of an arbitrary regular semigroup form a lattice. The properties of this lattice are investigated. 相似文献