On semigroup species

A countable directed family of semigroup congruences is introduced, and a theory analogous to the theory of normal series for groups is developed. This rather simple approach, surprisingly, is an effective tool for studying the structures of the lattices formed by certain species of semigroups (classes of semigroups closed under taking homomorphic images) such as varieties, pseudovarieties, and existence varieties etc.     

Maximal semigroup orbits

In this paper we show that certain actions are the a-homomorphic images of actions with disjoint maximal orbits. We also show that if T is a compact semigroup acting on a compact space X, then there is a compact right trivial semigroup Y and a congruenceN of T×Y such that (T×Y)/N homeomorphic to X and the action T×X→X is isomorphic the action of T on (T×Y)/N.     

正规Ehresmann型wrpp半群

众所周知,Clifford半群是正则半群类中的一类重要半群,本文定义正规 Ehresmann型wrpp半群,它是Clifford半群在wrpp半群类中的推广,给出了此类半群的若干刻划.     

P-完全正则半群

求证具有强半格结构的完全正则半群成为P-完全正则半群的充分条件.利用半群的强半格结构以及同余的性质.完全单半群的强半格-正规群带是P-完全正则半群.矩形群的强半格正规纯正群类ONBG,左群的强半格左正规纯整群类LONBG,群的强半格Clifford半群类,矩形带的强半格正规带类NB,都具有性质P.     

Two-point inequalities,the Hermite semigroup and the Gauss-Weierstrass semigroup

Let e^?zH, Re z ? 0, be the Hermite semigroup on R with Gauss measure μ. Necessary and sufficient conditions for e^?zH to be a bounded map from L^p(μ) into L^q(μ), 1 ? p, q ? ∞, are found and in many cases it is proved that e^?zH: L^p(μ) → L^q(μ) is in fact a contraction. Furthermore, these results and a formula relating the Hermite semigroup with the Gauss-Weierstrass semigroup e^zΔ enable one to calculate the precise norm of e^zΔ:L^p(dx) → L^q(dx) in a large number of cases.     

Embedding any countable semigroup in a 2-generated congruence-free semigroup

Communicated by N.R. Reilly     

Rank properties of the semigroup of endomorphisms over Brandt semigroup

We investigate small rank, lower rank, intermediate rank, upper rank, and large rank of the semigroup of endomorphisms over Brandt semigroup.     

半群的混沌作用

引进了半群混沌作用的概念,证明了若半群5在紧致度量空间X上的连续作用满足拓扑可迁和周期点稠两个条件,则此作用满足对初值的敏感依赖性,另外也讨论了半群S在X的逆极限空间上诱导作用的混沌性问题。