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1.
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
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3.
《代数通讯》2013,41(6):2447-2459
The aim of this paper is to study a class of rpp semigroups, namely the perfect rpp semigroups. We obtain some characterization theorems for such semigroups. In particular, the spined product structure of perfect rpp semigroups is established. As an application of spined product structure, we prove that a perfect rpp semigroup is a strong semilattice of left cancellative planks. By a left cancellative plank, we mean a product of a left cancellative monoid and a rectangular band. Thus, the work of J.B. Fountain on C-rpp semigroups is further developed. 相似文献
4.
A semigroup with zero isidempotent bounded (IB) if it is the 0-direct union of idempotent generated principal left ideals and the 0-direct union of idempotent generated principal right ideals. Notable examples are completely 0-simple semigroups and the wider class of primitive abundant semigroups. Significant to the structure of these semigroups is that they are all categorical at zero. In this paper we describe IB semigroups that are categorical at zero in terms ofdouble blocked Rees matrix semigroups. This generalises Fountain's characterisation of primitive abundant semigroups via blocked Rees matrix semigroups [1], which in turn yields the Rees theorem for completely 0-simple semigroups. 相似文献
5.
Norman R. Reilly 《Semigroup Forum》2012,84(1):176-199
In a manner similar to the construction of the fundamental group of a connected graph, this article introduces the construction
of a fundamental semigroup associated with a bipartite graph. This semigroup is a 0-direct union of idempotent generated completely
0-simple semigroups. The maximal nonzero subgroups are the corresponding fundamental groups of the connected components. Adding
labelled edges to the graph leads to a more general completely 0-simple semigroup. The basic properties of such semigroups
are examined and they are shown to have certain universal properties as illustrated by the fact that the free completely simple
semigroup on n generators and its idempotent generated subsemigroup appear as special cases. 相似文献
6.
Abundant Left C-lpp Proper Semigroups 总被引:2,自引:0,他引:2
Xiaojiang Guo 《Southeast Asian Bulletin of Mathematics》2000,24(1):41-50
The aim of this paper is to study a class of left abundant semigroups, so-called abundant left C-lpp proper semigroups including left type A proper semigroups and right inverse proper semigroups as its subclasses. A structure theorem similar to McAlisters for inverse proper semigroups is obtained. As its application, it is verified that any abundant left C-lpp proper semigroup can be embedded into a semidirect product of a left regular band by a cancellative monoid.AMS Subject Classification (1991): 20M10Suppoted by the Foundation of Yunnan University and also by the Director Foundation of Yunnan Province. 相似文献
7.
Wlpp semigroups are generalizations of lpp semigroups and regular semi-groups. In this paper, we consider some kinds of wlpp semigroups, namely right-e wlpp semigroups. It is proved that such a semigroup S , if and only if S is the strong semilattice of L-right cancellative planks;also if and only if S is a spined product of a right-e wlpp semigroup and a left normal band. 相似文献
8.
left order in Q and Q is a semigroup of left quotients of S if every q∈Q can be written as q=a^*b for some a, b∈S where a^* denotes the inverse of a in a subgroup of Q and if,
in addition, every square-cancellable element of S lies in a subgroup of Q. Perhaps surprisingly, a semigroup, even a commutative
cancellative semigroup, can have non-isomorphic semigroups of left quotients. We show that if S is a cancellative left order
in Q then Q is completely regular and the {\cal D}-classes of Q are left groups. The semigroup S is right reversible and its
group of left quotients is the minimum semigroup of left quotients of S.
The authors are grateful to the ARC for its generous financial support. 相似文献
9.
M. Satyanarayana 《Semigroup Forum》1971,3(1):43-50
A multiplicative semigroup S with 0 is said to be a R-semigroup if S admits a ring structure. Isbell proved that if a finitely
generated commutative semigroup is a R-semigroup, then it should be finite. The non-commutative version of this theorem is
unsettled. This paper considers semigroups, not necessarily commutative, which are principally generated as a right ideal
by single elements and semigroups which are generated by two independent generators and describes their structure. We also
prove that if a cancellative 0-simple semigroup containing an identity is a R-semigroup, then it should be a group with zero.
Communicated by A. H. Clifford 相似文献
10.
证明了ο-超富足半群S是正规密码ο-超富足半群当且仅当它是完全Jο-单半群的强半格.该结果也是正规密码超富足半群和正规密码群并半群分别在超富足半群和完全正则半群上的相应结构定理的推广。 相似文献
11.
《代数通讯》2013,41(6):2461-2479
Superabundant semigroups are generalizations of completely regular semigroups written the class of abundant semigroups. It has been shown by Fountain that an abundant semigroup is superabundant if and only if it is a semilattice of completely J *-simple semigroups. Reilly and Petrich called a semigroup S cryptic if the Green's relation H is a congruence on S. In this paper, we call a superabundant semigroup S a regular crypto semigroup if H * is a congruence on S such that S/H * is a regular band. It will be proved that a superabundant semigroup S is a regular crypto semigroup if and only if S is a refined semilattice of completely J *-simple semigroups. Thus, regular crypto semigroups are generalization of the cryptic semigroups as well as abundant semigroups. 相似文献
12.
Norman R. Reilly 《Semigroup Forum》2013,86(1):162-182
In a previous paper, the author showed how to associate a completely 0-simple semigroup with a connected bipartite graph containing labelled edges. In the main theorem, it is shown how these fundamental semigroups can be used to describe the regular principal factors of the free objects in certain Rees-Sushkevich varieties, namely, the varieties of semigroups that are generated by all completely 0-simple semigroups over groups in a variety of finite exponent. This approach is then used to solve the word problem for each of these varieties for which the corresponding group variety has solvable word problem. 相似文献
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P. G. Trotter 《Semigroup Forum》1972,5(1):1-13
Simple conditions are given in this paper that are sufficient to ensure the embeddability of a semigroup in a group. It is
shown that the class of semigroups satisfying the conditions properly contains the class of all cancellative left quasi-reversible
semigroups. 相似文献
15.
It is known that a C–rpp semigroup can be described as a strong
semilattice of left cancellative monoids. In this paper, we
introduce the class of left C–wrpp semigroups which includes the
class of left C–rpp semigroups as a subclass. We shall
particularly show that the semi-spined product of a left regular
band and a C–wrpp semigroup forms a curler which is a left
C–wrpp semigroup and vice versa. Results obtained by Fountain
and Tang on C–rpp semigroups are extended and strengthened. 相似文献
16.
Let A2 be the variety generated by the five-element non-orthodox 0-simple
semigroup. This paper presents the identity bases for several subvarieties of
A2 that are not generated by any completely 0-simple or completely simple
semigroups. It will be shown that several subvarieties of A2, including the
variety generated by the five-element Brandt semigroup, are hereditarily finitely
based. 相似文献
17.
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
18.
Guangtian Song 《Semigroup Forum》1995,51(1):295-298
LetR be a ring with identity,S be a semigroup with the set of idempotentsE(S), and denote (E(S)) for the subsemigroup ofS generated byE(S). In this paper, we prove that ifS is a semilattice of completely 0-simple semigroups and completely simple semigroups, then the semigroup ringRS possesses an identity iff so doesR(E(S)); especially, the result is true forS being a completely regular semigroup. 相似文献
19.
Mohammed Ali Faya Ibrahim 《Czechoslovak Mathematical Journal》2004,54(2):303-313
It was shown in [7] that any right reversible, cancellative ordered semigroup can be embedded into an ordered group and as a consequence, it was shown that a commutative ordered semigroup can be embedded into an ordered group if and only if it is cancellative. In this paper we introduce the concept of L-maher and R-maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered L or R-maher semigroup can be embedded into an ordered group. 相似文献
20.
将Green关系推广到Green~-关系。给出了密码^ ~ H-富足半群的半格分解,利用此分解,证明了^ ~ H-富足半群为正规密码^H-富足半群当且仅当它是完全^ ~ H-单半群的强半格. 相似文献