Let A = (A;F ) be an algebra and ConA its congruence lattice. Recall that A is congruence uniform (see e.g. [1], [5]) if for each Θ ∈ ConA and every a, b ∈ A, card[a]Θ = card[b]Θ. Examples of congruence uniform algebras are e.g. groups, rings or Boolean algebras. A variety V is congruence uniform if each A ∈ V has this property. It was proved by W. Taylor [5] that every congruence uniform varie...

Using a human-oriented formal example proof of the (lim +) theorem, i.e. that the sum of limits is the limit of the sum, which is of value for reference on its own, we exhibit a nonpermutability of β-steps and δ+-steps (according to Smullyan’s classification), which is not visible with non-liberalized δ-rules and not serious with further liberalized δ-rules, such as the δ+ + -rule. Besides a ca...

For a finite group G we define the graph Γ(G) to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes A, B are joined by an edge if for some A ∈ A, B ∈ B A and B permute. We characterise those groups G for which

Congruence among the Intended, Implemented and Attained “Thinking and Life Style” Curricula in the Eighth Grade M. A. Jamalifar Sh. Hashemi Moghadam, Ph.D. Z. Abedi Karajiban, Ph.D. A.R. Faghihi, Ph.D. The present study was carried out to examine the congruence among the intended, implemented and attained “thinking and life style” curricula in th...

A general notion of a congruence system is introduced for π-institutions. Congruence systems in this sense are collections of equivalence relations on the sets of sentences of the π-institution that are preserved both by signature morphisms and by fixed collections of natural transformations from finite tuples of sentences to sentences. Based on this notion of a congruence system, the notion of...

In this note, we introduce the concept of a fuzzy filter of a BLalgebra,with respect to a t-norm briefly, T-fuzzy filters, and give some relatedresults. In particular, we prove Representation Theorem in BL-algebras. Thenwe generalize the notion of a fuzzy congruence (in a BL-algebra) was definedby Lianzhen et al. to a new fuzzy congruence, specially with respect to a tnorm.We prove that there i...

Work status congruence is the extent to which employees’ current work status (full time or part time) is congruent with their desired work status (Maynard, Thorsteinson & Parfyonova, 2006). Work status incongruence occurs when employees’ work status is inconsistent with their preferred work status, i.e., they are working full time but prefer to work part time or they are working part time but p...