Complete Congruences on the Lattice of Rees–Sushkevich Varieties

We study the lattice ?(RS_n) of subvarieties of the variety of semigroups generated by completely 0-simple semigroups over groups with exponent dividing n, with a particular focus on the lattice ??(RS_n) consisting of those varieties that are generated by completely 0-simple semigroups. The sublattice of ??(RS_n) consisting of the aperiodic varieties is described and several endomorphisms of ?(RS_n) considered. The complete congruence on ??(RS_n) that relates varieties containing the same aperiodic completely 0-simple semigroups is considered in some detail.     

Prime Ideals of Cancellative Semigroups

Abstract

For a class of prime ideals P of a cancellative semigroup S it is shown that the factors S/P have a structure of a monomial semigroup over a group. Consequences for the semigroup algebras K[S] are discussed.     

分子格半群

在本文中，作者在格半群上引入了半群元和理想元的概念，使得半群（理想）和ＴＬ－Ｆｕｚｚｙ半群（理想）是其特例。在分子格半群上引入了群元和正规群元等概念，在更高的层次上统一了群和Ｌ－Ｆｕｚｚｙ群。     

Approximate amenability of Banach category algebras with application to semigroup algebras

Let C be a small category. Then we consider ℓ ¹(C) as the ℓ ¹ algebra over the morphisms of C, with convolution product and also consider as the ℓ ¹ algebra over the objects of C, with pointwise multiplication. The main purpose of this paper is to show that approximate amenability of ℓ ¹(C) implies of and clearly this implies that C has only finitely many objects. Some applications are given, the main one is the characterization of approximate amenability for ℓ ¹(S), where S is a Brandt semigroup, which corrects a result of Lashkarizadeh Bami and Samea (Semigroup Forum 71:312–322, 2005).     

Toric degeneration of branching algebras

For each classical symmetric pair (G,H), there is a naturally defined multi-graded algebra , called the branching algebra for (G,H), which encodes the branching rule from G to H. This algebra has a natural family of subalgebras, depending on integer parameters. For a certain range of the parameters, the subalgebras have a particularly simple structure and are called stable branching algebras.In this paper, we show that the stable branching algebras for eight out of the ten families of classical symmetric pairs are flat deformations of the semigroup algebras of explicitly described lattice cones.     

Thickness of Feathers

Briefly, a feather is a semigroup derivation diagram with the labels on the edges removed. In this paper, we are concerned with possible definitions for the thickness of a feather.

A major open problem is whether the word problem is solvable for semigroup presentations with one defining relation. It is known that word problems for semigroup presentations are solvable if the number of regions in minimal derivation diagrams is bounded. For some definitions for thickness, the number of regions in a derivation diagram over a presentation with one relation will be bounded if the thickness of the diagram is bounded.     

Generation of the integrated semigroups by superelliptic differential operators

Let A be a superelliptic differential operator of order 2m introduced by E.B. Davies [E.B. Davies, Uniformly elliptic operators with measurable coefficients, J. Funct. Anal. 132 (1995) 141-169]. In the case of 2m>N, he obtained the upper Gaussian bound of the integral kernel representing (e−zA)_z∈C+ and the estimates of the Lp-operator norm of the semigroup for all p∈[1,∞). The purpose of the present paper is to show that −i(A+k) (for some constant k>0) generates an integrated semigroup on Lα,p (weighted Lp space) and lp(Lα,q). To prove this we need norm estimates of (e−zA)_z∈C+ on each of these spaces. Also we get another norm estimate of (e−zA)_z∈C+ on Lp when 2m>N without using the integral kernel. This norm estimate is better than that in [E.B. Davies, Uniformly elliptic operators with measurable coefficients, J. Funct. Anal. 132 (1995) 141-169] and gives a better “times of the integration” of the integrated semigroup.     

Embedding the bicyclic semigroup into countably compact topological semigroups

We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p,q). We prove that a topological semigroup S with pseudocompact square contains no dense copy of C(p,q). On the other hand, we construct a (consistent) example of a pseudocompact (countably compact) Tychonoff semigroup containing a copy of C(p,q).     

Classification of Rota-Baxter operators on semigroup algebras of order two and three

In this paper, we determine all the Rota-Baxter operators of weight zero on semigroup algebras of order two and three with the help of computer algebra. We determine the matrices for these Rota-Baxter operators by directly solving the defining equations of the operators. We also produce a Mathematica procedure to predict and verify these solutions.     

由格蕴涵代数诱导的伴随半群

给出由格蕴涵代数诱导出的伴随半群及有关概念 ,详细讨论伴随半群中的元素即格蕴涵代数的左映射的性质 ,得到它们的几个等价条件。最后讨论由格蕴涵代数诱导的两个双格半群与伴随半群之间的关系 ,并证明这些半群是幂等的当且仅当它们是由格 H蕴涵代数所诱导     

Iterative Algebras without Projections

We deal with iterative algebras of functions of -valued logic lacking projections, which we call algebras without projections. It is shown that a partially ordered set of algebras of functions of -valued logic, for , without projections contains an interval isomorphic to the lattice of all iterative algebras of functions of -valued logic. It is found out that every algebra without projections is contained in some maximal algebra without projections, which is the stabilizer of a semigroup of non-surjective transformations of the basic set. It is proved that the stabilizer of a semigroup of all monotone non-surjective transformations of a linearly ordered 3-element set is not a maximal algebra without projections, but the stabilizer of a semigroup of all transformations preserving an arbitrary non one-element subset of the basic set is.     

关于余弦算子函数的一个结果

设Ａ是Ｂａｎａｃｈ空间Ｘ中的闭线性算子,对凡　是单射。文中定义了Ｂａｎａｃｈ空间　范数　强于Ｘ的范数。我们证明了算子Ａ在空间Ｚ中的部分ＡＺ生成Ｚ中的一个余弦算子函数,空间Ｚ具有某种意义上的极大性。     

Distances between elements of a semigroup and estimates for derivatives

This paper is concerned first with the behaviour of differences T（t） - T（s） near the origin, where （T（t）） is a semigroup of operators on a Banach space, defined either on the positive real line or a sector in the right half-plane （in which case it is assumed analytic）. For the non-quasinilpotent case extensions of results in the published literature are provided, with best possible constants; in the case of quasinilpotent semigroups on the half-plane, it is shown that, in general, differences such as T（t） -T（2t） have norm approaching 2 near the origin. The techniques given enable one to derive estimates of other functions of the generator of the semigroup; in particular, conditions are given on the derivatives near the origin to guarantee that the semigroup generates a unital algebra and has bounded generator.     

Filters in (Quasiordered) Semigroups and Lattices of Filters

A filter in a semigroup is a subsemigroup whose complement is an ideal. (Alternatively, in a quasiordered semigroup, a slightly more general definition can be given.) We prove a number of results related to filters in a semigroup and the lattice of filters of a semigroup. For instance, we prove that every complete algebraic lattice can be the lattice of filters of a semigroup. We prove that every finite semigroup is a homomorphic image of a finite semigroup whose lattice of filters is boolean and which belongs to the pseudovariety generated by the original semigroup. We describe filter lattices of some well-known semigroups such as full transformation semigroups of finite sets (which are three-element chains) and free semigroups (which are boolean).     

On Lattice-ordered Rees Matrix Semigroups

ＯｎＬａｔｔｉｃｅ－ｏｒｄｅｒｅｄＲｅｅｓＭａｔｒｉｘＳｅｍｉｇｒｏｕｐｓ￥（谢祥云）ＸｉｅＸｉａｎｇｙｕｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＬａｎｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｚｈｏｕ，７３００００）Ａｂｓｔｒａｃｔ：Ｔｈｅｐ...     

Matrix semigroup homomorphisms into higher dimensions

We study non-degenerate irreducible homomorphisms from the multiplicative semigroup of all n-by-n matrices over an algebraically closed field of characteristic zero to the semigroup of m-by-m matrices over the same field. We prove that every non-degenerate homomorphism from the multiplicative semigroup of all n-by-n matrices to the semigroup of (n + 1)-by-(n + 1) matrices when n ? 3 is reducible and that every non-degenerate homomorphism from the multiplicative semigroup of all 3-by-3 matrices to the semigroup of 5-by-5 matrices is reducible.     

关于半群环与群环的链条件的等价性

给出了将半群环的链条件转化为群环的链条件的一个定理,并由此将［１］中的结果推广到半群环的情形．