اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدRepresentations of inverse semigroups in complete atomistic inverse meet-semigroups
146
0
0.0
(
0
)
تأليف
D. G. FitzGerald
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
As an appropriate generalisation of the features of the classical (Schein) theory of representations of inverse semigroups in $mathscr{I}_{X}$, a theory of representations of inverse semigroups by homomorphisms into complete atomistic inverse algebras is developed. This class of inverse algebras includes partial automorphism monoids of entities such as graphs, vector spaces and modules. A workable theory of decompositions is reached; however complete distributivity is required for results approaching those of the classical case.
قيم البحث
اقرأ أيضاً
We find necessary and sufficient conditions on an (inverse) semigroup $X$ under which its semigroups of maximal linked systems $lambda(X)$, filters $phi(X)$, linked upfamilies $N_2(X)$, and upfamilies $upsilon(X)$ are inverse.
A new construction of a free inverse semigroup was obtained by Poliakova and Schein in 2005. Based on their result, we find a Groebner-Shirshov basis of a free inverse semigroup relative to the deg-lex order of words. In particular, we give the (uniq
ue and shortest) Groebner-Shirshov normal forms in the classes of equivalent words of a free inverse semigroup together with the Groebner-Shirshov algorithm to transform any word to its normal form.
This note proves a generalisation to inverse semigroups of Anisimovs theorem that a group has regular word problem if and only if it is finite, answering a question of Stuart Margolis. The notion of word problem used is the two-tape word problem -- t
he set of all pairs of words over a generating set for the semigroup which both represent the same element.
First we give a definition of a coverage on a inverse semigroup that is weaker than the one gave by a Lawson and Lenz and that generalizes the definition of a coverage on a semilattice given by Johnstone. Given such a coverage, we prove that there ex
ists a pseudogroup that is universal in the sense that it transforms cover-to-join idempotent-pure maps into idempotent-pure pseudogroup homomorphisms. Then, we show how to go from a nucleus on a pseudogroup to a topological groupoid embedding of the corresponding groupoids. Finally, we apply the results found to study Exels notions of tight filters and tight groupoids.
A congruence on an inverse semigroup $S$ is determined uniquely by its kernel and trace. Denoting by $rho_k$ and $rho_t$ the least congruence on $S$ having the same kernel and the same trace as $rho$, respectively, and denoting by $omega$ the univers
al congruence on $S$, we consider the sequence $omega$, $omega_k$, $omega_t$, $(omega_k)_t$, $(omega_t)_k$, $((omega_k)_t)_k$, $((omega_t)_k)_t$, $cdots$. The quotients ${S/omega_k}$, ${S/omega_t}$, ${S/(omega_k)_t}$, ${S/(omega_t)_k}$, ${S/((omega_k)_t)_k}$, ${S/((omega_t)_k)_t}$, $cdots$, as $S$ runs over all inverse semigroups, form quasivarieties. This article explores the relationships among these quasivarieties.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
