We study congruences on the partial automorphism monoid of a finite rank free group action. determine decomposition congruence this into Rees congruence, Brandt semigroup and an idempotent separating congruence. The constituent parts are further described in terms subgroups direct semidirect products groups. utilize description to demonstrate how number depends

The Independence Theorem for the congruence lattice and the auto-morphism group of a nite lattice was proved by V. A. Baranski and A. Urquhart. Both proofs utilize the characterization theorem of congruence lattices of nite lattices (as nite distributive lattices) and the characterization theorem of auto-morphism groups of nite lattices (as nite groups). In this paper, we introduce a new, stron...

An ω-language over a finite alphabet X is a set of infinite sequences of letters of X. Previously studied syntactic equivalence relations defined by ω-languages have mainly been relations on X∗. In this paper the emphasis is put on relations in Xω, by associating to an ω-language L a congruence on Xω, called the ω-syntactic congruence of L. Properties of this congruence and notions induced by i...

Since congruence modulo m is an equivalence relation, it partitions the universe of integers into equivalence classes, which we’ll call congruence classes modulo m. Within any one of these classes, all of the members are congruent to all of the other members; but congruence modulo m never holds between members of different equivalence classes. For instance, there are two congruence classes modu...

It is evident from the definition that the class of all BCK-algebras is a quasivariety. Yet it is not a variety, nor does the largest subvariety of BCK exist—as shown in Wroński [2], Kabziński & Wroński [3], respectively. Several subvarieties of BCK have been isolated and thoroughly investigated, which has led to a substantial body of results (cf. e.g., Blok & Raftery [4]). Nevertheless, the qu...

Congruence is the degree to which one’s personality matches one’s behavior in a particular situation. On four separate occasions over several weeks, 202 undergraduate participants described a situation they encountered the previous day and their behavior. Analyses considered overall congruence as well as distinctive congruence, adjusted for the match of personality and behavior to the normative...

We investigate the degree of congruence between preferred and actual levels of ten management control system (MCS) practices in the areas of budgeting, performance evaluation, and compensation. Survey results from responsibility centre managers indicate significant disagreements between preferred and actual levels for most MCS practices. Congruence states of deprivation, satisfaction, and satur...

We prove that a minimal automaton has a minimal adjacency matrix rank and a minimal adjacency matrix nullity using equitable partition (from graph spectra theory) and Nerode partition (from automata theory). This result naturally introduces the notion of matrix rank into a regular language L, the minimal adjacency matrix rank of a deterministic automaton that recognises L. We then define and fo...

We propose a method for realising the proofs of Intuitionistic Zermelo-Fraenkel set theory (IZF) by strongly normalising λ-terms. This method relies on the introduction of a Curry-style type theory extended with specific subtyping principles, which is then used as a low-level language to interpret IZF via a representation of sets as pointed graphs inspired by Aczel’s hyperset theory. As a conse...