Some Reducibility Properties for Pseudovarieties of the Form Drh
نویسنده
چکیده
Let H be a pseudovariety of groups and DRH be the pseudovariety containing all finite semigroups whose regular R-classes belong to H. We study the relationship between reducibility of H and of DRH with respect to several particular classes of systems of equations. The classes of systems considered (of pointlike, idempotent pointlike and graph equations) are known to play a role in decidability questions concerning pseudovarieties of the forms V ∗W, V ∨W, and V©m W.
منابع مشابه
Complete Reducibility of Pseudovarieties
The notion of reducibility for a pseudovariety has been introduced as an abstract property which may be used to prove decidability results for various pseudovariety constructions. This paper is a survey of recent results establishing this and the stronger property of complete reducibility for specific pseudovarieties.
متن کاملOn reducibility of weighted composition operators
In this paper, we study two types of the reducing subspaces for the weighted composition operator $W: frightarrow ucdot fcirc varphi$ on $L^2(Sigma)$. A necessary and sufficient condition is given for $W$ to possess the reducing subspaces of the form $L^2(Sigma_B)$ where $Bin Sigma_{sigma(u)}$. Moreover, we pose some necessary and some sufficient conditions under which the subspaces of the form...
متن کاملFree Profinite Semigroups Over Some Classes of Semigroups Locally in D(G)
The theory of free profinite semigroups, which received its major impetus with the publication of Reiterman’s paper [17] in the early eighties, has proven to be an important tool in the study of pseudovarieties of semigroups and on the varieties of recognizable languages associated with them (via Eilenberg’s Theorem on varieties [13]). The importance of Reiterman’s theorem was immediately under...
متن کاملReducibility of Pointlike Problems
We show that the pointlike and the idempotent pointlike problems are reducible with respect to natural signatures in the following cases: the pseudovariety of all finite semigroups in which the order of every subgroup is a product of elements of a fixed set π of primes; the pseudovariety of all finite semigroups in which every regular J-class is the product of a rectangular band by a group from...
متن کاملSome Algorithmic Problems for Pseudovarieties
Several algorithmic problems for pseudovarieties and their relationships are studied. This includes the usual membership problem and the computability of pointlike subsets of nite semi-groups. Some of these problems aaord equivalent formulations involving topological separation properties in free proonite semigroups. Several examples are considered and, as an application, a decidability result ...
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 2015