共查询到20条相似文献,搜索用时 0 毫秒
1.
Translated from Algebra i Logika, Vol. 28, No. 4, pp. 371–381, July–August, 1989. 相似文献
2.
This paper continues the study begun in [GEROLDINGER, A.: On non-unique factorizations into irreducible elements II, Colloq. Math. Soc. János Bolyai 51 (1987), 723–757] concerning factorization properties of block monoids of the form ℬ(ℤ
n
, S) where S =
(hereafter denoted ℬ
a
( n)). We introduce in Section 2 the notion of a Euclidean table and show in Theorem 2.8 how it can be used to identify the irreducible elements of ℬ
a
( n). In Section 3 we use the Euclidean table to compute the elasticity of ℬ
a
( n) (Theorem 3.4). Section 4 considers the problem, for a fixed value of n, of computing the complete set of elasticities of the ℬ
a
( n) monoids. When n = p is a prime integer, Proposition 4.12 computes the three smallest possible elasticities of the ℬ
a
( p).
Part of this work was completed while the second author was on an Academic Leave granted by the Trinity University Faculty
Development Committee. 相似文献
3.
In questo articolo, si dimostra il legame fra la semi-fattorialità e la fattorialità debole nel contesto degli ordini algebrici.
In particolare, si ottiene che un ordine semi-fattoriale ha il stesso numero di classi che su chiusura integrale. 相似文献
4.
Squier (1987) showed that if a monoid is defined by a finite complete rewriting system, then it satisfies the homological
finiteness condition FP 3, and using this fact he gave monoids (groups) which have solvable word problems but cannot be presented by finite complete
systems. In the present paper we show that a monoid cannot have a finite complete presentation if it contains certain special
elements. This observation enables us to construct monoids without finite complete presentation in a direct and elementary
way. We give a finitely presented monoid which has (1) a word problem solvable in linear time and (2) linear growth but (3)
no finite complete presentation. We also give a finitely presented monoid which has (1) a word problem solvable in linear
time, (2) finite derivation type in the sense of Squier and (3) the property FP ∞, but (4) no finite complete presentation. 相似文献
5.
This paper addresses conditions under which all generators in the category of right S-acts (where S is a monoid) satisfy a flatness property. There are characterizations for monoids over which all generators satisfy a flatness property α where α can stand for freeness, projectivity, strong flatness, Condition (P), principal weak flatness and torsion freeness. To our knowledge, the problem has not been studied for other flatness properties such as weak flatness, Condition (E) and regularity. The present paper addresses this gap. 相似文献
6.
The difference in length between two distinct factorizations of an element in a Dedekind domain or in the corresponding block
monoid is an object of study in the theory of non-unique factorizations. It provides an alternate way, distinct from what
the elasticity provides, of measuring the degree of non-uniqueness of factorizations. In this paper, we discuss the difference
in consecutive lengths of irreducible factorizations in block monoids of the form where . We will show that the greatest integer r, denoted by , which divides every difference in lengths of factorizations in can be immediately determined by considering the continued fraction of . We then consider the set including necessary and sufficient conditions (which depend on p) for a value to be an element of .
2000 Mathematics Subject Classification Primary—20M14, 11A55, 20D60, 11A51
Parts of this work are contained in the first author’s Doctoral Dissertation written at the University of North Carolina at
Chapel Hill under the direction of the third author. 相似文献
7.
A new characterization of monoids over which all strongly flat cyclic right acts are projective (projective generators, free)
is given.
This research has been supported by the Estonian Science Foundation, Grant No. 930. 相似文献
9.
An integral domain is said to be a half-factorial domain (HFD) if every non-zero element a that is not a unit may be factored into a finite product of irreducible elements, while any other such factorization of a has the same number of irreducible factors. While it is known that a power series extension of a factorial domain need not be factorial, the corresponding question for HFD has been open. In this paper we show that the answer is also negative. In the process we answer in the negative, for HFD, an open question of Samuel for factorial domains by showing that for certain quadratic domains R, and independent variables, Y and T, R[[ Y]][[ T]] is not HFD even when R[[ Y]] is HFD. The proof hinges on Samuel’s theorem to the effect that a power series, in finitely many variables, over a regular factorial domain is factorial. 相似文献
12.
We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups and their relatives acting on monoids of set partitions. The nature of our monoids indicate that they should give origin to new knot algebras; indeed, our tied monoids include the tied braid monoid and the tied singular braid monoid, which were used, respectively, to construct new polynomial invariants for classical links and singular links. Consequently, we provide a mechanism to attach an algebra to each tied monoid; this mechanism not only captures known generalizations of the bt-algebra, but also produces possible new knot algebras. To build the tied monoids it is necessary to have presentations of set partition monoids of types A, B and D, among others. For type A we use a presentation due to FitzGerald and for the other type it was necessary to built them. 相似文献
14.
Abstract. No abstract. 相似文献
16.
It is proved that in the variety of positive Sugihara monoids, every finite subdirectly irreducible algebra is a retract of
a free algebra. It follows that every quasivariety of positive Sugihara monoids is a variety, in contrast with the situation
in several neighboring varieties. This result shows that when the logic R-mingle is formulated with the Ackermann constant t, then its full negation-free fragment is hereditarily structurally complete.
Presented by R. W. Quackenbush.
Received August 28, 2005; accepted in final form July 31, 2006. 相似文献
17.
Factorizable inverse monoids constitute the algebraic theory of those partial symmetries which are restrictions of automorphisms;
the formal definition is that each element is the product of an idempotent and an invertible. This class of monoids has theoretical
significance, and includes concrete instances which are important in various contexts. This survey is organised around the
idea of group acts on semilattices and contains a large range of examples. Topics also include methods for construction of
factorizable inverse monoids, and aspects of their inner structure, morphisms, and presentations. 相似文献
20.
In this paper, we define and study what we call the double Catalan monoid. This monoid is the image of a natural map from the 0-Hecke monoid to the monoid of binary relations. We show that the double Catalan monoid provides an algebraization of the (combinatorial) set of 4321-avoiding permutations and relate its combinatorics to various off-shoots of both the combinatorics of Catalan numbers and the combinatorics of permutations. In particular, we give an algebraic interpretation of the first derivative of the Kreweras involution on Dyck paths, of 4321-avoiding involutions and of recent results of Barnabei et al. on admissible pairs of Dyck paths. We compute a presentation and determine the minimal dimension of an effective representation for the double Catalan monoid. We also determine the minimal dimension of an effective representation for the 0-Hecke monoid. 相似文献
|