the aim of this paper is to extend results established by h. onoand t. kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. the main theorem states that a residuatedlattice a is directly indecomposable if and only if its boolean center b(a)is {0, 1}. we also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...

We show that a locally finite variety is congruence join semidistributive if and only if it satisfies a congruence identity that is strong enough to force join semidistributivity in any lattice.

The congruence between the order of cladistic branching and the first appearance dates of fossil lineages can be quantified using a variety of indices. Good matching is a prerequisite for the accurate time calibration of trees, while the distribution of congruence indices across large samples of cladograms has underpinned claims about temporal and taxonomic patterns of completeness in the fossi...

Let V be a congruence distributive variety, or a congruence modular variety whose free algebra on 2 generators is finite. If V is residually small and has the amalgamation property, then it has the congruence extension property. Several applications are presented. In two previous papers [1] and [2], we considered the following question: if V is a residually small variety with the amalgamation p...

A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto elements. We show that the binary trees whose leaves are labeled by letters alphabet containing at least three letters, a if and only polynomial.

Taxonomic congruence and total evidence are competing paradigms in phylogenetic inference. Taxonomic congruence focuses on deriving a consensus from the results obtained from separately analyzed data sets, whereas total evidence uses character congruence in the search for the best-fitting hypothesis for all of the available character evidence. Explicit or implicit use of taxonomic congruence is...

Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the topological features of congruence relations among natural numbers. Here, we explore the congruence relations in the setting of a multiplex network and unveil s...