Relative congruence distributivity within quasivarieties of nearly associative Φ-algebras

Universal Quasivarieties of Algebras

Two different notions of universal, one due to Hedrlín and Pultr in the 1960s and the other due to Sapir in the 1980s, are discussed, as well as the relationship between them. Some of the historical perspective and mathematical motivation lying behind them is also included, together with a brief overview of a variety meriting further investigation in this context.

Congruence Distributivity Implies Bounded Width

We show that a constraint language with compatible Jónnson terms (i.e. associated with an algebra generating a congruence distributive variety) defines a Constraint Satisfaction Problem solvable by the local consistency checking algorithm.

Relatively Congruence Modular Quasivarieties of Modules

We show that the quasiequational theory of a relatively congruence modular quasivariety of left R-modules is determined by a two-sided ideal in R together with a filter of left ideals. The two-sided ideal encodes the identities that hold in the quasivariety, while the filter of left ideals encodes the quasiidentities. The filter of left ideals defines a generalized notion of torsion. It follows...

Ideals in Quasivarieties of Algebras

On Certain Quasivarieties of Quasi-MV Algebras

Quasi-MV algebras are generalisations of MV algebras arising in quantum computational logic. Although a reasonably complete description of the lattice of subvarieties of quasi-MV algebras has already been provided, the problem of extending this description to the setting of quasivarieties has so far remained open. Given its apparent logical repercussions, we tackle the issue in the present pape...