Quasiorders and Sublattices of Distributive Lattices

We study the lattice of all (0,1)-sublattices of a distributive lattice L, using certain compatible quasiorders on the Priestley space of L as our principal tool. Special emphasis is put on the case of finite L, where epic sublattices, Frattini sublattices and covers are considered in some detail. We hope to demonstrate that quasiorders may serve as a concept suitable to unify the many different representations of sublattices of L which are found in the literature.     

Tiling Lattices with Sublattices,I

Call a coset C of a subgroup of Z^d{\bf Z}^{d} a Cartesian coset if C equals the Cartesian product of d arithmetic progressions. Generalizing Mirsky–Newman, we show that a non-trivial disjoint family of Cartesian cosets with union Z^d{\bf Z}^{d} always contains two cosets that differ only by translation. Where Mirsky–Newman’s proof (for d=1) uses complex analysis, we employ Fourier techniques. Relaxing the Cartesian requirement, for d>2 we provide examples where Z^d{\bf Z}^{d} occurs as the disjoint union of four cosets of distinct subgroups (with one not Cartesian). Whether one can do the same for d=2 remains open.     

Sublattices of Lattices of Convex Subsets of Vector Spaces

Let Co(V) be a lattice of convex subsets of a vector space V over a totally ordered division ring . We state that every lattice L can be embedded into Co(V), for some space V over . Furthermore, if L is finite lower bounded, then V can be taken finite-dimensional; in this case L also embeds into a finite lower bounded lattice of the form Co(V,)={X | X Co(V)}, for some finite subset of V. This result yields, in particular, a new universal class of finite lower bounded lattices.     

Block-separating Congruence Lattices of E-bisimple Semigroups

In this paper,we study block-separating congruences on E-bisimple semigroups. We describe two congruence relations T and W on the lattice of block-separating congruences, where the latter is defined in this paper. We determine the greatest and smallest congruences in T-classes and W-classes.     

P-反演半群上的强P-同余

本文介绍了P-反演半群S(P)的概念，借助于核与迹刻画了P-反演半群上的强P-同余，并且证明了S(P)上的任一强P-同余可以决定S(P)的一个强P-同余对，反之S(P)的任一强P-同余对，可以决定S(P)上的一个强P-同余.     

Block Separating Congruence Lattices of E－bisimple Semigroups

In 1966, Reilly Characterized bisimple ω-semigroups as Bruck-Reilly extensions of Groups.Later, Munn and Reilly proved that a congruence on a bisimple ω-semigroup is a group congruence or is idempotent-separating. Many author investigated the congruences on Bruck-Reilly ex-     

交换半群的强半格

本文刻划交换半群的强半格上的最小半格同余，并证明由此得到的商半群为对应的每个交换半群的商半群的强半格。     

Triviality of the Peripheral Point Spectrum of Positive Semigroups on Atomic Banach Lattices

Generalizing a result of Keicher [4] we show that generators of positive C ₀-semigroups on super-atomic Banach lattices have trivial peripheral point spectrum provided they satisfy a certain growth condition.     

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).     

P-反演半群上强P-同余的P-核正规系

Let S(P) be a P-inversive semigroup. In this paper we describe the strong P-congruences on S(P) in terms of their P-kernel normal systems. We prove that any strong P-congruence on S(P) can present a P-kernel normal system; conversely any P-kernel normal system of S(P) can determine a strong P-congruence.     

带逆断面的正则半群上的强模糊同余

带逆断面的正则半群是一类重要的正则半群.就带逆断面的正则半群类引入强模糊同余的概念,进而用所谓的强模糊同余三元组抽象地刻画带逆断面的正则半群上的强模糊同余.     

Representation of Finite Lattices by Annihilators of Completely 0-Simple Semigroups

L the explicit construction of a 0-simple Rees matrix semigroup is suggested such that the lattice of left annihilators of this semigroup is isomorphic to L.     

Spectral Properties of a Class of Positive Semigroups on Banach Lattices and Streaming Operators

We deal with a general streaming semigroup arising in transport theory. We show that in general such a semigroup has a direct decomposition into three simpler semigroups one of which extends to a group. A general spectral theory of them is given and is partly derived from that of a class of positive semigroups on Banach lattices.     

Strong Wedderburn Decompositions of Banach Algebras Containing Analytic Semigroups

We prove that if a Banach algebra contains an analytic semigroupwhich satisfies a certain growth condition then neither it norany homomorphic image of it may have a Strong Wedderburn Decomposition,in particular it must be weakly amenable.     

非Lipschitz仿射映射的半拓扑半群的强遍历定理(英)

本文在Banach空间中给出了非Lipschitzian仿信射拓扑半群的强遍历定理。