共查询到20条相似文献,搜索用时 31 毫秒
1.
On the weak regularity of semigroup rings 总被引:2,自引:0,他引:2
Fang Li 《Semigroup Forum》1994,48(1):152-162
Sufficient conditions are obtained under which the semigroup ring of a semigroup, in particular, of an inverse semigroup, is weakly regular. For some inverse semigroups and some orthodox semigroups, the necessary and sufficient conditions for the weak regularity of the semigroup rings are found. A problem is mentioned especially which is much more difficult for weak regularity than for regularity. Only a partial solution of this problem is given for weak regularity. 相似文献
2.
Within the class of regular E-solid semigroups, a theory of e-varieties including appropriate notions of biidentities and biinvariant congruences is presented, such that, together with bifree objects, these notions inherit the properties and interrelations well known from universial algebra. This theory generalizes the previously developed such theory for orthodox semigroups. As an application, the bifree objects in certain e-varieties of E-solid locally orthodox semigroups, which are constructed by means of Malcev products from a varities of bands, groups and completely simple semigroups, are described as subsemigroups in suitable Pastijn products of some bands by relatively bifree completely simple semigroups. As a consequence, it follows that every regular E-solid locally orthodox semigroup regularly divides a so-called solid Pastijn product of a band by a completely simple semigroup. 相似文献
3.
Orthodox semigroups whose idempotents satisfy a certain identity 总被引:2,自引:0,他引:2
Miyuki Yamada 《Semigroup Forum》1973,6(1):113-128
An orthodox semigroup S is called a left [right] inverse semigroup if the set of idempotents of S satisfies the identity xyx=xy
[xyx=yx]. Bisimple left [right] inverse semigroups have been studied by Venkatesan [6]. In this paper, we clarify the structure
of general left [right] inverse semigroups. Further, we also investigate the structure of orthodox semigroups whose idempotents
satisfy the identity xyxzx=xyzx. In particular, it is shown that the set of idempotents of an orthodox semigroup S satisfies
xyxzx=xyzx if and only if S is isomorphic to a subdirect product of a left inverse semigroup and a right inverse semigroup. 相似文献
4.
We investigate certain semigroup varieties formed by nilpotent extensions of
orthodox normal bands of commutative periodic groups. Such semigroups are shown
to be both structurally periodic and structurally commutative, and are therefore
structurally inverse semigroups. Such semigroups are also shown to be dense
semilattices of structurally group semigroups. Making use of these structure
decompositions, we prove that the subvariety lattice of any variety comprised of
such semigroups is isomorphic to the direct product of the following three
sublattices: its sublattice of all structurally trivial semigroup varieties, its
sublattice of all semilattice varieties, and its sublattice of all group
varieties. We conclude, therefore, that to completely describe this lattice, we
must first describe completely the lattice of all structurally trivial semigroup
varieties, since the other two are well known lattices. 相似文献
5.
6.
Note on a certain class of orthodox semigroups 总被引:1,自引:0,他引:1
Miyuki Yamada 《Semigroup Forum》1973,6(1):180-188
This is a continuation and also a supplement of the previous papers [5], [6] and [8] concerning orthodox semigroups1). In [8], it has been shown that a quasi-inverse semigroup is isomorphic to a subdirect product of a left inverse semigroup
and a right inverse semigroup. In this paper, we present a structure theorem for quasi-inverse semigroups and some relevant
matters. 相似文献
7.
A semigroup S is called a Clifford semigroup if it is completely regular and inverse. In this paper, some relations related to the least
Clifford semigroup congruences on completely regular semigroups are characterized. We give the relation between Y and ξ on completely regular semigroups and get that Y
* is contained in the least Clifford congruence on completely regular semigroups generally. Further, we consider the relation
Y
*, Y, ν and ε on completely simple semigroups and completely regular semigroups.
This work is supported by Leading Academic Discipline Project of Shanghai Normal University, Project Number: DZL803 and General
Scientific Research Project of Shanghai Normal University, No. SK200707. 相似文献
8.
Mária B. Szendrei 《Semigroup Forum》1980,20(1):1-10
In the present paper we deal with two problems concerning orthodox semigroups. M. Yamada raised the questions in [6] whether
there exists an orthodox semigroup T with band of idempotents E and greatest inverse semigroup homomorphic image S for every
band E and inverse semigroup S which have the property that
is isomorphic to the semilattice of idempotents of S, and if T exists then whether it is always unique up to isomorphism.
T. E. Hall [1] has published counter-examples in connection with both questions and, moreover, he has given a necessary and
sufficient condition for existence. Now we prove a more effective necessary and sufficient condition for existence and deal
with uniqueness, too. On the other hand, D. B. McAlister's theorem in [4] saying that every inverse semigroup is an idempotent
separating homomorphic image of a proper inverse semigroup is generalized for orthodox semigroups. The proofs of these results
are based on a theorem concerning a special type of pullback diagrams. In verifying this theorem we make use of the results
in [5] which we draw up in Section 1. The main theorems are stated in Section 2. For the undefined notions and notations the
reader is referred to [2]. 相似文献
9.
We study a class of special strongly rpp semigroups, namely, the class of super rpp semigroups. These super rpp semigroups
are generalizations of both superabundant semigroups and Clifford semigroups within the class of rpp semigroups. In particular,
we prove that a super rpp semigroup is a semilattice of D
(l)-simple strongly rpp semigroups. Our result not only generalizes a well-known theorem of Clifford in the class of completely
regular semigroups but also strengthens some structure theorems obtained by Ren-Shum for superabundant semigroups which are
orthodox. Some special super rpp semigroups are considered and discussed. 相似文献
10.
本文在正则半群上引入弱中间幂等元和拟中间幂等元,着重探讨了这两类幂等元的性质特征.构造了若干具有弱(拟)中间幂等元的正则半群,确定了弱中间幂等元和拟中间幂等元之间的关系,给出了弱中间幂等元和拟中间幂等元各自的等价判定,利用拟中间幂等元刻画了纯正半群.最后,得到了构造具有拟中间幂等元的正则半群的一般途径,并在此基础上进一步给出了判定正则半群是否具有乘逆断面的方法. 相似文献
11.
12.
The notion of an inverse transversal of a regular semigroup is well-known. Here we investigate naturally ordered regular semigroups
that have an inverse transversal. Such semigroups are necessarily locally inverse and the inverse transversal is a quasi-ideal.
After considering various general properties that relate the imposed order to the natural order, we highlight the situation
in which the inverse transversal is a monoid. The regularity of Green’s relations is also characterised. Finally, we determine
the structure of a naturally ordered regular semigroup with an inverse monoid transversal. 相似文献
13.
《数学学报(英文版)》2015,(7)
A semigroup is called completely J~((e))-simple if it is isomorphic to some Rees matrix semigroup over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid.It is proved that completely J~((e))-simple semigroups form a quasivarr ity.Moreover,the construction of free completely J~((e))-simple semigroups is given.It is found that a free completely J~((e))-simple semigroup is just a free completely J~*-simple semigroup and also a full subsemigroup of some completely simple semigroups. 相似文献
14.
15.
Free completely <Emphasis Type="Italic">J</Emphasis><Superscript>(<Emphasis Type="Italic">ℓ</Emphasis>)</Superscript>-simple Semigroups 下载免费PDF全文
A semigroup is called completely J(ι)-simple if it is isomorphic to some Rees matrix semigroup over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid. It is proved that completely J(ι)-simple semigroups form a quasivarity. Moreover, the construction of free completely J(ι)-simple semigroups is given. It is found that a free completely J(ι)-simple semigroup is just a free completely J *-simple semigroup and also a full subsemigroup of some completely simple semigroups. 相似文献
16.
Igor Dolinka 《Journal of Pure and Applied Algebra》2009,213(10):1979-1990
We show that a finite completely regular semigroup has a sub-log-exponential free spectrum if and only if it is locally orthodox and has nilpotent subgroups. As a corollary, it follows that the Seif Conjecture holds true for completely regular monoids. In the process, we derive solutions of word problems of free objects in a sequence of varieties of locally orthodox completely regular semigroups from solutions of word problems in relatively free bands. 相似文献
17.
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
18.
19.
Every inverse semigroup possesses a natural partial order and therefore convexity with respect to this order is of interest.
We study the extent to which an inverse semigroup is determined by its lattice of convex inverse subsemigroups; that is, if
the lattices of two inverse semigroups are isomorphic, how are the semigroups related? We solve this problem completely for
semilattices and for inverse semigroups in general reduce it to the case where the lattice isomorphism induces an isomorphism
between the semilattices of idempotents of the semigroups. For many inverse semigroups, such as the monogenic ones, this case
is the only one that can occur. In Part II, a study of the reduced case enables us to prove that many inverse semigroups,
such as the free ones, are strictly determined by their lattices of convex inverse subsemigroups, and to show that the answer
obtained here for semilattices can be extended to a broad class of inverse semigroups, including all finite, aperiodic ones.
Received September 24, 2002; accepted in final form December 15, 2002. 相似文献
20.
具有拟理想正则*-断面的正则半群 总被引:4,自引:1,他引:3
本文提出了具有正则*-断面正则半群的概念,所给出的例子表明具有拟理想正则*-断面的正则半群类真包含了具有拟理想逆断面的正则半群类和正则*-半群类;最后刻画了具有拟理想正则*-断面的正则半群的结构. 相似文献