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1.
《代数通讯》2013,41(7):2803-2826
Abstract A transformation semigroup over a set X with N elements is said to be a near permutation semigroup if it is generated by a group of permutations on N elements and by a set of transformations of rank N ? 1. The aim of this paper is to determine computationally efficient conditions to test whether or not a near permutation semigroup is regular. 相似文献
2.
A semigroup is regular if it contains at least one idempotent in each ?-class and in each ?-class. A regular semigroup is inverse if it satisfies either of the following equivalent conditions: (i) there is a unique idempotent in each ?-class and in each ?-class, or (ii) the idempotents commute. Analogously, a semigroup is abundant if it contains at least one idempotent in each ?*-class and in each ?*-class. An abundant semigroup is adequate if its idempotents commute. In adequate semigroups, there is a unique idempotent in each ?* and ?*-class. M. Kambites raised the question of the converse: in a finite abundant semigroup such that there is a unique idempotent in each ?* and ?*-class, must the idempotents commute? In this note, we provide a negative answer to this question. 相似文献
3.
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
4.
Jorge M. André 《代数通讯》2013,41(10):3607-3617
5.
The structure of superabundant semigroups 总被引:9,自引:0,他引:9
K.P.Shum 《中国科学A辑(英文版)》2004,47(5):756-771
A structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for superabundant semigroups but also generalizes the well-known result of Petrich on completely regular semigroups. Some results obtained by Fountain on abundant semigroups are also extended and strengthened. 相似文献
6.
The concept of super hamiltonian semigroup is introduced. As a result, the structure theorems obtained by A. Cherubini and A. Varisco on quasi commutative semi-groups and quasi hamiltonian semigroups respectively are extended to super hamiltonian semigroups. 相似文献
7.
Attila Nagy 《Semigroup Forum》2008,76(2):297-308
We say that a semigroup S is a permutable semigroup if the congruences of S commute with each other, that is, α○β=β○α is satisfied for all congruences α and β of S. A semigroup is called a medial semigroup if it satisfies the identity axyb=ayxb. The medial permutable semigroups were examined in Proc. Coll. Math. Soc. János Bolyai, vol. 39, pp. 21–39 (1981), where the medial semigroups of the first, the second and the third kind were characterized, respectively. In Atta Accad.
Sci. Torino, I-Cl. Sci. Fis. Mat. Nat. 117, 355–368 (1983) a construction was given for medial permutable semigroups of the second [the third] kind. In the present paper we give a
construction for medial permutable semigroups of the first kind. We prove that they can be obtained from non-archimedean commutative
permutable semigroups (which were characterized in Semigroup Forum 10, 55–66, 1975).
Research supported by the Hungarian NFSR grant No T042481 and No T043034. 相似文献
8.
9.
Benjamin Steinberg 《Semigroup Forum》2008,76(3):584-586
We prove the pseudovariety generated by power semigroups of completely simple semigroups is the semidirect product of the
pseudovariety of block groups with the pseudovariety of right zero semigroups, and hence is decidable. This answers a question
of Almeida from over 15 years ago.
The author was supported in part by NSERC. 相似文献
10.
A new class of semigroups with a two variable regularity law is introduced. These semigroups are non-regular semigroups but they are closely related to regular semigroups. The local and global structures of this class of semigroups are investigated.AMS Subject Classification (2000): 20M10Partially supported by a Chinese University of Hong Kong Direct Research grant, Hong Kong (98/99) # 2060152.Partially supported by a grant of the National Science Foundation, China. 相似文献
11.
12.
R. Exel 《Semigroup Forum》2009,79(1):159-182
By a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse
semigroup
in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of
Booleanness present in the semilattice of idempotents of
. After observing that the Vagner–Preston representation is not tight, we exhibit a canonical tight representation for any
inverse semigroup with zero, called the regular tight representation. We then tackle the question as to whether this representation is faithful, but it turns out that the answer is often negative.
The lack of faithfulness is however completely understood as long as we restrict to continuous inverse semigroups, a class generalizing the E
*-unitaries.
Partially supported by CNPq. 相似文献
13.
On a mathematical model of age‐cycle length structured cell population with non‐compact boundary conditions
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Mohamed Boulanouar 《Mathematical Methods in the Applied Sciences》2015,38(11):2081-2104
This work deals with a mathematical model of an age‐cycle length structured cell population. Each cell is distinguished by its age and its cycle length. The cellular mitosis is mathematically described by non‐compact boundary conditions. We prove then that this mathematical model is governed by a positive C0‐semigroup. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
14.
Yupaporn Kemprasit 《Southeast Asian Bulletin of Mathematics》2002,25(4):617-622
Let V and W be vector spaces over a division ring D and LD (V, W) the set of all linear transformations from V into W. For LD(W, V), let (LD (V, W), ) denote the semigroup LD (V, W) with the operation * defined by * = for all , LD(V, W). By a unit-regular semigroup we mean a semigroup S with identity having the property that for each a S, a = aua for some unit u S. The main purpose of this paper is to prove the following statements. The semigroup (LD(V, W), ) is regular if and only if V = {0}, W = {0} or is an isomorphism from W onto V. The semigroup (LD (V, W), ) is unit-regular if and only if (i) V = {0}, (ii) W = {0} or (iii) is an isomorphism from W onto V and dimD V . 相似文献
15.
SHUM Kar Ping 《中国科学A辑(英文版)》2009,(2)
As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semi-groups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in HU on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup WU and a V-ample semigroup ... 相似文献
16.
J. C. Rosales P. A. Garcia-Sanchez J. I. Garcia-Garcia M. B. Branco 《Czechoslovak Mathematical Journal》2005,55(3):755-772
We study numerical semigroups S with the property that if m is the multiplicity of S and w(i) is the least element of S congruent with i modulo m, then 0 < w(1) < ... < w(m − 1). The set of numerical semigroups with this property and fixed multiplicity is bijective with an affine semigroup and
consequently it can be described by a finite set of parameters. Invariants like the gender, type, embedding dimension and
Frobenius number are computed for several families of this kind of numerical semigroups.
This paper was supported by the project BFM2000-1469. The fourth author wishes to acknowledge support from the Universidade
de Evora and the CIMA-UE. 相似文献
17.
设A是代数闭域k上的一个具乘基B的有限维含幺结合代数,称半群B∪{0}为A的基半群.本文给出了0 J 严格单半群的定义.对于基半群为0 J 严格单半群的零直并的代数,完全研究了它的代数表示型 相似文献
18.
Let S be a cancellation torsion-free additive semigroup with identity 0 and let S {0}. We consider the relation between the valuation ideals and primary ideals of S. We give a characterization that each primary ideal is a valuation ideal in S and also give a characterization that each valuation ideal is a primary ideal in S.AMS Subject Classification (1991): 20M14 相似文献
19.
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
20.
On a mathematical model of age‐cycle length structured cell population with non‐compact boundary conditions (III)
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Mohamed Boulanouar 《Mathematical Methods in the Applied Sciences》2016,39(1):73-91
This work is a natural continuation of two other works in which a mathematical model has been studied. This model is based on age‐cycle length structured cell population. The cellular mitosis is mathematically described by a non‐compact boundary condition. We investigate the asymptotic behavior of the generated semigroup, and we prove that the cell population possesses Asynchronous Growth Property. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献