Necessary Isomorphism Conditions for Rogers Semilattices of Finite Partially Ordered Sets

We establish a condition that is necessary for Rogers semilattices of computable numberings of finite families of computably enumerable sets to be isomorphic.     

阿基米德序半群的链(英文)

本文通过一个序半群S上的一些二元关系以及它的理想(右理想,双理想)的根集分别给出了该序半群是阿基米德(右阿基米德,t-阿基米德)序子半群的链的刻画.进一步证明了准素序半群是阿基米德序半群的链.最后,通过素根定理证明了序半群S是阿基米德序子半群的链当且仅当S是阿基米德序子半群的半格且S的所有素理想关于集合的包含关系构成链.     

Semilattice Operations Generated by Lattice Terms

Let ℒ=〈L;∨,∧〉 be a subdirectly irreducible modular lattice, c∈L and p(x,y,z) an essentially ternary lattice term. In this paper we show that if p(x,y,c) is a semilattice operation then p(x,y,c)=∨ or ∧ and L is bounded and c=0 or c=1. This sheds light on the methodology used to move back and forth between generalizations of median algebras and lattices, and provides a negative answer to a problem posed by A. Knoebel and G. Meletiou. Mathematics Subject Classifications (2000) Primary 06A12, 06C99, 08B26.     

Semilattices of Nil-extensions of Simple Regular Semigroups

Semigroups decomposable into a semilattice of Archimedean semigroups, having certain additional properties such as the intra-, left, right and complete -regularity, have been investigated in many papers. In the present paper, we study the -regular ones. Among other things, we characterize them as semilattices of nil-extensions of simple regular semigroups. The obtained results generalize some results given by Munn, Putcha, Shevrin, Bogdanovi, iri, and others.2000 Mathematics Subject Classification: 20M10, 20M17     

Semilattices of Definable Subalgebras

In issues bearing on the structure of universal algebras , derived structures, such as automorphism groups Aut , subalgebra lattices Sub , congruence lattices Con , etc., play an important part. On the other hand, in studying universal algebras by the means of model theory, of crucial importance is the question asking which elements of the derived structures under examination are expressible by one or other formulas in the elementary language. Problems concerning the interrelationship of algebras and their derived structures are treated for subalgebras of universal algebras.Supported by RFBR grant No. 02-01-00258.__________Translated from Algebra i Logika, Vol. 44, No. 4, pp. 474–482, July–August, 2005.     

The hyperspace of the regions below of all lattice-value continuous maps and its Hilbert cube compactification

Let L be a continuous semilattice. We use USC(X, L) to denote the family of all lower closed sets including X × {0} in the product space X × AL and ↓1 C(X,L) the one of the regions below of all continuous maps from X to AL. USC(X, L) with the Vietoris topology is a topological space and ↓C(X, L) is its subspace. It will be proved that, if X is an infinite locally connected compactum and AL is an AR, then USC(X, L) is homeomorphic to [-1,1]ω. Furthermore, if L is the product of countably many intervals, then ↓ C(X, L) is homotopy dense in USC(X,L), that is, there exists a homotopy h : USC(X,L) × [0,1] →USC(X,L) such that h0 = idUSC(X,L) and ht(USC(X,L)) C↓C(X,L) for any t > 0. But ↓C(X, L) is not completely metrizable.     

几类亚交换序半群

本文研究几类亚交换序半群的性质,并将具有单位元的亚交换序半群的一些结果扩张到这几类亚交换序半群上,使得这些结果更加细化,其中主要证明了以下定理：伪交换序半群可以分解成阿基米德序半群的半格．并且,一般来说,这种分解不是唯一的．     

乘法半群为左正规纯正群的半环

研究了加法半群为半格,乘法半群为左正规纯正群的半环．证明了此类半环（S,＋,．）可以嵌入到半格（S,＋）的自同态半环中．构造S的一个特定的偏序关系,得到了（S,·）上的自然偏序与所构造偏序相等的等价条件．     

Non-Complementedness and Non-Distributivity of Kleene Degrees

In this note, we study the complementedness and the distributivity of upper semilattices of Kleene degrees assuming V = L. K denotes the upper semilattice of all Kleene degrees. We prove that if V = L, then some sub upper semilattices of K are non-complemented and some are non-distributive.