共查询到20条相似文献,搜索用时 15 毫秒
1.
J. C. Rosales 《代数通讯》2013,41(3):1362-1367
Every almost symmetric numerical semigroup can be constructed by removing some minimal generators from an irreducible numerical semigroup with its same Frobenius number. 相似文献
2.
We generalize the geometric sequence {ap, ap?1b, ap?2b2,…, bp} to allow the p copies of a (resp. b) to all be different. We call the sequence {a1a2a3… ap, b1a2a3…ap, b1b2a3…ap,…, b1b2b3…bp} a compound sequence. We consider numerical semigroups whose minimal set of generators form a compound sequence, and compute various semigroup and arithmetical invariants, including the Frobenius number, Apéry sets, Betti elements, and catenary degree. We compute bounds on the delta set and the tame degree. 相似文献
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4.
Monica Madero-Craven 《代数通讯》2013,41(10):3831-3838
Let S be a numerical semigroup. We examine a particular subset of the Apery set of S and establish a correspondence between this subset and the holes of S . This correspondence allows us to establish conditions for S to be almost symmetric. 相似文献
5.
We study two-dimensional irreducible projective smooth algebraic semigroups. Minimal surface semigroups with Kodaira dimension at most one are partially classified. We also calculate the local dimension of the moduli scheme parameterizing all algebraic semigroup laws on a fixed minimal surface. 相似文献
6.
Trae Holcomb 《代数通讯》2013,41(7):2496-2508
This article completes a previous investigation of balanced and unitary numerical semigroups. The main result establishes the equivalence of unitary numerical semigroups and perfect 2 × 2 bricks. 相似文献
7.
For a numerical semigroup, we introduce the concept of a fundamental gap with respect to the multiplicity of the semigroup. The semigroup is fully determined by its multiplicity and these gaps.We study the case when a set of non-negative integers is the set of fundamental gaps with respect to the multiplicity of a numerical semigroup, Numerical semigroups with maximum and minimum number of this kind of gaps are described. 相似文献
8.
For a numerical semigroup, we introduce the concept of a fundamental gap with respect tothe multiplicity of the semigroup.The semigroup is fully determined by its multiplicity and these gaps.We study the case when a set of non-negative integers is the set of fundamental gaps with respect to themultiplicity of a numerical semigroup.Numerical semigroups with maximum and mininmm number ofthis kind of gaps are described. 相似文献
9.
This article considers numerical semigroups S that have a nonprincipal relative ideal I such that μ S (I)μ S (S ? I) = μ S (I + (S ? I)). We show the existence of an infinite family of such pairs (S, I) in which I + (S ? I) = S\{0}. We also show examples of such pairs that are not members of this family. We discuss the computational process used to find these examples and present some open questions pertaining to them. 相似文献
10.
《代数通讯》2013,41(12):4713-4731
Abstract Let S be a numerical semigroup and let I be a relative ideal of S. Let S ? I denote the dual of I and let μ S (?) represent the size of a minimal generating set. We investigate the inequality μ S (I)μ S (S ? I) ≥ μ S (I + (S ? I)) under the assumption that S has multiplicity 8. We will show that if I is non-principal, then the strict inequality μ S (I)μ S (S ? I) > μ S (I + (S ? I)) always holds. 相似文献
11.
Kyle Siegrist 《Journal of Theoretical Probability》2006,19(1):204-220
Let (S,·) be a positive semigroup and T a sub-semigroup of S. In many natural cases, an element can be factored uniquely as x=yz, where and where z is in an associated “quotient space” S/T. If X has an exponential distribution on S, we show that Y and Z are independent and that Y has an exponential distribution on T. We prove a converse when the sub-semigroup is for . Specifically, we show that if Y
t
and Z
t
are independent and Y
t
has an exponential distribution on S
t
for each , then X has an exponential distribution on S. When applied to ([0,∞), +) and , these results unify and extend known results on the quotient and remainder when X is divided by t. 相似文献
12.
Dario Spirito 《代数通讯》2013,41(7):2943-2963
It is proved that the number of numerical semigroups with a fixed number n of star operations is finite if n > 1. The result is then extended to the class of analytically irreducible residually rational one-dimensional Noetherian rings with finite residue field and integral closure equal to a fixed discrete valuation domain. 相似文献
13.
Let W be an injective unilateral weighted shift, and let W(n) be the orthogonal direct sum of n copies of W. In this paper, we prove that, if the commutant of W is strictly cyclic, then W(n) has a unique (SI) decomposition with respect to similarity for every natural number n. 相似文献
14.
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
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Automatic Completely-Simple Semigroups 总被引:2,自引:0,他引:2
C. M. Campbell E. F. Robertson M. Ruškuc R. M. Thomas 《Acta Mathematica Hungarica》2002,95(3):201-215
The notion of automaticity has been widely studied in groups and some progress has been made in understanding the notion in the wider context of semigroups. The purpose of this paper is to study automatic completely-simple semigroups. We show that, if
is a completely-simple semigroup
(with
and
finite), then
is automatic if and only if the group
is automatic. As a consequence, we deduce that automatic completely-simple semigroups are finitely presented. We also show that automatic completely-simple semigroups are characterized by the fellow traveller property and also that the existence of an automatic structure is independent of the choice of generating set. 相似文献
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18.
If S is a semigroup, the global (or the power semigroup) of S is the set P(S) of all nonempty subsets of S equipped with a naturally defined multiplication. A class K of semigroups is globally determined if any two semigroups of K with isomorphic globals are themselves isomorphic. We study properties of globals of idempotent semigroups and show, in particular, that the class of normal bands is globally determined. 相似文献
20.
完全单半群及完全正则半群的逆断面 总被引:1,自引:1,他引:0
指出完全单半群S的任何一个F-类是逆断面,且为Q-逆断面,而S的任何一个逆断面必是一个F-类,因而所有逆断面同构。并且给出完全正则半群的逆断面存在的充要条件。 相似文献