共查询到20条相似文献,搜索用时 31 毫秒
1.
J. C. Rosales P. A. García-Sánchez J. I. García-García J. A. Jiménez Madrid 《Semigroup Forum》2003,67(1):145-158
We study the set of numerical semigroups containing a given numerical semigroup. As an application we prove characterizations of irreducible numerical semigroups that unify some of the existing characterizations for symmetric and pseudo-symmetric numerical semigroups. Finally we describe an algorithm for computing a minimal decomposition of a numerical semigroup in terms of irreducible numerical semigroups. 相似文献
2.
A semigroup S is said to be n-central if xn belongs to the center of S for every x S. We prove that every n-central semigroup is a semilattice of archimedean n-central semigroups. We obtain characterizations of simple (0-simple) n-central semigroups and describe subdirectly irreducible n-central semigroups. We also deal with the connection of n-central semigroups and E-k semigroups. 相似文献
3.
AbstractIn this paper we introduce the notion of extension of a numerical semigroup. We provide a characterization of the numerical semigroups whose extensions are all arithmetic and we give an algorithm for the computation of the whole set of arithmetic extension of a given numerical semigroup. As by-product, new explicit formulas for the Frobenius number and the genus of proportionally modular semigroups are obtained. 相似文献
4.
Víctor Blanco 《Semigroup Forum》2013,87(2):407-427
In this paper we analyze the irreducibility of numerical semigroups with multiplicity up to four. Our approach uses the notion of Kunz-coordinates vector of a numerical semigroup recently introduced in Blanco and Puerto (SIAM J. Discrete Math., 26(3):1210–1237, 2012). With this tool we also completely describe the whole family of minimal decompositions into irreducible numerical semigroups with the same multiplicity for this set of numerical semigroups. We give detailed examples to show the applicability of the methodology and conditions for the irreducibility of well-known families of numerical semigroups such as those that are generated by a generalized arithmetic progression. 相似文献
5.
In this paper we introduce the concept of modular translation. With this tool, if we consider a certain numerical semigroup S, we build another one S′ whose principal invariants are given explicitly in terms of the invariants of S. Some results about irreducible numerical semigroups are also studied. 相似文献
6.
In this paper we consider the Schwarz radical of linear algebraic semigroups as defined in semigroup theory. We give some new characterizations of the complete regularity, regularity and solvability of irreducible linear algebraic monoids in terms of Schwarz radical data. Moreover, we give a generalization about the results of the kernel to the results of completely regular \(\mathscr {J}\)-classes. 相似文献
7.
In this paper, the translational hull of a type B semigroup is considered. We prove that the translational hull of a type B
semigroup is itself a type B semigroup, and give some properties and characterizations of the translational hulls of such
semigroups. Moreover, we consider the translational hulls of some special type B semigroups. These results strengthen the
results of Fountain and Lawson (Semigroup Forum 32:79–86, 1985) on adequate semigroups. Finally, we give a new proof of a problem posted by Petrich on translational hulls of inverse semigroups
in Petrich (Inverse Semigroups, Wiley, New York, 1984). 相似文献
8.
We give characterizations of different classes of ordered semigroups by using intuitionistic fuzzy ideals. We prove that an
ordered semigroup is regular if and only if every intuitionistic fuzzy left (respectively, right) ideal of S is idempotent. We also prove that an ordered semigroup S is intraregular if and only if every intuitionistic fuzzy two-sided ideal of S is idempotent. We give further characterizations of regular and intra-regular ordered semigroups in terms of intuitionistic
fuzzy left (respectively, right) ideals. In conclusion of this paper we prove that an ordered semigroup S is left weakly regular if and only if every intuitionistic fuzzy left ideal of S is idempotent. 相似文献
9.
《代数通讯》2013,41(8):2929-2948
Abstract A semigroup S is called E-inversive if for every a ∈ S there is an x ∈ S such that ax is idempotent. The purpose of this paper is the investigation of E-inversive semigroups and semigroups whose idempotents form a subsemigroup. Basic properties are analysed and, in particular, semigroups whose idempotents form a semilattice or a rectangular band are considered. To provide examples and characterizations, the construction methods of generalized Rees matrix semigroups and semidirect products are employed. 相似文献
10.
In this article we prove that if S is an irreducible numerical semigroup and S is generated by an interval or S has multiplicity 3 or 4, then it enjoys Toms decomposition. We also prove that if a numerical semigroup can be expressed as an expansion of a numerical semigroup generated by an interval, then it is irreducible and has Toms decomposition. 相似文献
11.
12.
本文通过一个序半群S上的一些二元关系以及它的理想(右理想,双理想)的根集分别给出了该序半群是阿基米德(右阿基米德,t-阿基米德)序子半群的链的刻画.进一步证明了准素序半群是阿基米德序半群的链.最后,通过素根定理证明了序半群S是阿基米德序子半群的链当且仅当S是阿基米德序子半群的半格且S的所有素理想关于集合的包含关系构成链. 相似文献
13.
Motivated by studying fuzzy congruences in groups, semigroups, and ordered semigroups, and as a continuation of N. Kuroki and Y. Tan's works in regular semigroups in terms of fuzzy subsets, in this article we introduce the notions of a fuzzy good congruence relation, a fuzzy cancellative congruence relation on abundant semigroups, and give some properties, and characterizations of fuzzy good congruences on such semigroups. Furthermore, we characterize fuzzy good congruences of left semiperfect abundant semigroups, and get sufficient and necessary conditions for an abundant semigroup to be left semiperfect. 相似文献
14.
We study groups and semigroups of n x n matrices with the property that each matrix has a fixed point, i.e., 1 is an eigenvalue of each matrix. We show that for n=3 and $n\geq 5$ there are irreducible matrix groups and irreducible semigroups of nonnegative matrices with this property. In fact, for n = 3 we determine the structure of any such semigroup. We also present additional hypotheses implying reducibility. 相似文献
15.
Yufei Zhao 《Semigroup Forum》2010,80(2):242-254
Let n g denote the number of numerical semigroups of genus g. Bras-Amorós conjectured that n g possesses certain Fibonacci-like properties. Almost all previous attempts at proving this conjecture were based on analyzing the semigroup tree. We offer a new, simpler approach to counting numerical semigroups of a given genus. Our method gives direct constructions of families of numerical semigroups, without referring to the generators or the semigroup tree. In particular, we give an improved asymptotic lower bound for n g . 相似文献
16.
Abstract. In this paper we investigate the structure of semigroups with the ideal retraction property i.e., semigroups which are not
simple and have the property that each ideal is a homomorphic retract of the semigroup.
We present examples to show that the ideal retraction property is neither hereditary nor productive. That this property is
preserved by homomorphisms is established for some classes of semigroups, but the general question remains open.
The classes of semigroups investigated in this paper are separative semigroups, ideal semigroups, semilattices, cyclic semigroups,
nil semigroups, and Clifford semigroups.
It is established that a semigroup with zero 0 which is expressible as a direct sum of each ideal and a dual ideal (complement
with 0 adjoined) has the ideal retraction property. The converse holds for ideal semigroups, and an example is presented which
demonstrates that the converse does not hold in general. 相似文献
17.
R. A. R. Monzo 《Semigroup Forum》1973,6(1):59-68
This investigation was stimulated by a question raised by F.R. McMorris and M. Satyanarayana [Proc. Amer. Math. Soc.
33 (1972), 271–277] which asked whether a regular semigroup with a tree of idempotents is categorical. The question is answered
in the affirmative. Characterizations of categorical semigroups are found within the following classes of semigroups: regular
semigroups, bands, commutative regular semigroups, unions of simple semigroups, semilattices of groups, and commutative semigroups.
Some results are related to part of the work of M. Petrich [Trans. Amer. Math. Soc.
170 (1972), 245–268]. For instance, it is shown that the poset of J-classes of any regular categorical semigroup is a tree; however,
an example of a regular non-categorical semigroup is given in which the poset of J-classes is a chain.
It is also shown that the condition that the subsemigroup of idempotents be categorical is sufficient, but not necessary,
for an orthodox semigroup to be categorical. 相似文献
18.
Primoz Moravec 《Semigroup Forum》2006,73(1):143-155
A semigroup is said to be power centralized if for every pair of elements x and y there exists a power of x commuting with
y. The structure of power centralized groups and semigroups is investigated. In particular, we characterize 0-simple power
centralized semigroups and describe subdirectly irreducible power centralized semigroups. Connections between periodic semigroups
with central idempotents and periodic power commutative semigroups are discussed. 相似文献
19.
Benjamin Steinberg 《Advances in Mathematics》2010,223(2):689-727
Let K be a commutative ring with unit and S an inverse semigroup. We show that the semigroup algebra KS can be described as a convolution algebra of functions on the universal étale groupoid associated to S by Paterson. This result is a simultaneous generalization of the author's earlier work on finite inverse semigroups and Paterson's theorem for the universal C∗-algebra. It provides a convenient topological framework for understanding the structure of KS, including the center and when it has a unit. In this theory, the role of Gelfand duality is replaced by Stone duality.Using this approach we construct the finite dimensional irreducible representations of an inverse semigroup over an arbitrary field as induced representations from associated groups, generalizing the case of an inverse semigroup with finitely many idempotents. More generally, we describe the irreducible representations of an inverse semigroup S that can be induced from associated groups as precisely those satisfying a certain “finiteness condition.” This “finiteness condition” is satisfied, for instance, by all representations of an inverse semigroup whose image contains a primitive idempotent. 相似文献
20.
A proportionally modular numerical semigroup is the set of nonnegative integer solutions to a Diophantine inequality of the
type ax mod b ≤ cx. We give a new presentation for these semigroups and we relate them with a type of affine full semigroups.
Next, we describe explicitly the minimal generating system for the affine full semigroups
we are considering. As a consequence, we obtain generating systems for proportionally modular numerical semigroups and we
exhibit several families of these semigroups in terms of their generators. Finally, we use the concept of fundamental gap
to study when a proportionally modular numerical semigroup is symmetric and we propose some open problems. 相似文献