右消去幺半群、左正则带和左正则型A幺半群

本文利用右消去幺半群,左正则带建立了真左正则型A幺半群．在证明了任一左正则型A幺半群均有P－覆盖后,给出P－覆盖的结构．     

On the Lattice of Overcommutative Varieties of Monoids

We study the lattice of varieties of monoids, i.e., algebras with two operations, namely, an associative binary operation and a 0-ary operation that fixes the neutral element. It was unknown so far, whether this lattice satisfies some non-trivial identity. The objective of this paper is to give the negative answer to this question. Namely, we prove that any finite lattice is a homomorphic image of some sublattice of the lattice of overcommutative varieties of monoids (i.e., varieties that contain the variety of all commutative monoids). This implies that the lattice of overcommutative varieties of monoids, and therefore, the lattice of all varieties of monoids does not satisfy any non-trivial identity.     

On Graph Products of Automatic and Biautomatic Monoids

It is shown that the graph product of automatic monoids is always automatic thereby improving on a result by Veloso da Costa [22] who showed this result provided the factors have finite geometric type. Secondly, we prove that, in general, the free product (and therefore the graph product) of biautomatic monoids need not be biautomatic. Imposing a restriction on the factors that is symmetric to Veloso da Costa's "finite geometric type", the biautomaticity of all graph products of biautomatic monoids is shown.     

On Identity Bases of Exclusion Varieties for Monoids

An exclusion variety is a variety that is maximal with respect to not containing some semigroup. It is shown that if the bases of all exclusion varieties for some periodic semigroup S are known, then the bases of exclusion varieties for the monoid S ¹ can be computed.     

Frattini Theory for Classes of Finite Universal Algebras of Malcev Varieties

We extend the Frattini theory of formations and Schunck classes of finite groups to some Frattini theory of formations and Schunck classes of finite universal algebras of Malcev varieties. We prove that if F(1) is a nonempty formation (Schunck class) of algebras of a Malcev variety, then its Frattini subformation (Frattini Schunck subclass) (F) consists of all nongenerators of F; moreover, if M is a formation (Schunck class) in F; then (M) (F).     

Varieties Generated by Ordered Bands II

The lattice of all subvarieties of the variety generated by all ordered bands is obtained. This lattice is distributive and contains 78 varieties precisely. Each of these is finitely based and generated by a finite number of finite ordered bands.     

Varieties Generated by Ordered Bands I

Ordered bands are regarded as semirings whose multiplicative reduct is a band and whose additive reduct is a chain. We find the variety of semirings generated by all ordered bands and we determine part of the lattice of its subvarieties.     

All Varieties of Normal Bands with Involution

In the present paper we completely determine the lattice L(NB ^*) of all varieties of normal bands equipped with an involutorial antiautomorphism as a fundamental operation.     

右（左）逆半群的半直积及圈积

给出了两个幺半群的半直积及圈积为右（左）逆半群的充分必要条件，从而推广了[2]中两个幺半群的半幺直积和圈积为逆半群的充分必要条件．     

Structures of Malcev Bialgebras on a Simple Non-Lie Malcev Algebra

In this work we consider Malcev bialgebras. We describe all structures of a Malcev bialgebra on a simple non-Lie Malcev algebra.     

Minimal but Inefficient Presentations of the Semi-Direct Products of Some Monoids

Abstract. In recent papers of Ruskuc, Saito and J. Wang, the semi-direct product of two arbitrary monoids and a standard presentation, say P, for this product have received considerable attention. Wang defined a trivialiser set of the Squier complex associated with P and after that necessary and sufficient conditions for P to be efficient have been given by Cevik. As a main result of this paper, we give sufficient conditions for a presentation of the semi-direct product of a one-relator monoid by an infinite cyclic monoid to be minimal but not efficient . In the final part of this paper we give some applications of this result.     

Monoids and decay

We propose some formalization of the concept of critical decay number and describe the class of models with this number at most 4 (i.e., every object is decomposable which consists of four or more elements).     

关于Malcev代数的幂零性

We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M)=M D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal Ⅰ(A) = A D(A, M)is nilpotent in L(M).     

The Composition Structure of Alternative and Malcev Algebras

We construct a polynomial of degree 5 from the associative nucleus (kernel) of the free alternative algebra. We show that this polynomial is of minimal degree. Using this polynomial, we obtain decompositions of the varieties of alternative and Malcev algebras.