Two Operators on the Lattice of Completely Regular Semigroup Varieties
نویسندگان
چکیده
In this paper, varieties of completely regular semigroups are studied. This paper is divided into six sections. Section 1 contains an introduction to varieties of completely regular semigroups and preliminaries. Most of the notation needed in this paper is given. In Section 2, the operators ←− ( ) and −→ ( ) on the lattice of subvarieties of varieties of completely regular semigroups are investigated. In Section 3, some further properties of the operators ←− ( ) and −→ ( ) are given. In Section 4, the semigroups generated by various subset of some operators are considered. In Section 5, the operators ←− ( ) and −→ ( ) are used in finding the join of two given varieties. The word problem for free objects in the variety OLBG is considered in Section 6 using the operator ←− ( ) .
منابع مشابه
On the join of two pseudovarieties
The aim of this lecture is to survey some recent developments in the theory of finite semigroups. More precisely, we shall consider the following problem about pseudovarieties of semigroups: given two pseudovarieties V and W, find a description of their join V ∨W (that is, of the pseudovariety they generate). This question is motivated by the theory of rational languages: it appears in a natura...
متن کاملA classification of hull operators in archimedean lattice-ordered groups with unit
The category, or class of algebras, in the title is denoted by $bf W$. A hull operator (ho) in $bf W$ is a reflection in the category consisting of $bf W$ objects with only essential embeddings as morphisms. The proper class of all of these is $bf hoW$. The bounded monocoreflection in $bf W$ is denoted $B$. We classify the ho's by their interaction with $B$ as follows. A ``word'' is a function ...
متن کاملSpecial Elements in the Lattice of Overcommutative Semigroup Varieties Revisited
We completely determine all distributive, codistributive, standard, costandard, and neutral elements in the lattice of overcommutative semigroup varieties, thus correcting a gap contained in [5].
متن کاملThe Wreath Product of Atoms of the Lattice of Semigroup Varieties
A semigroup variety is called a Cross variety if it is finitely based, is generated by a finite semigroup, and has a finite lattice of subvarieties. It is established in which cases the wreath product of two semigroup varieties each of which is an atom of the lattice of semigroup varieties is a Cross variety. Furthermore, for all the pairs of atoms U and V for which this is possible, either a f...
متن کاملCongruence semimodular varieties II: Regular varieties
In [8], P. Jones characterized the regular varieties of semigroups which are congruence semimodular and he partially solved the problem of characterizing the non-regular, congruence semimodular (CSM) varieties of semigroups. For regular varieties his characterization was an equational one, so necessarily a part of his argument was semigroup-theoretic. But some of his argument involved only cong...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002