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Some regular quasivarieties of commutative binary modes

K. Matczak, Anna B. Romanowska (2014)

Commentationes Mathematicae Universitatis Carolinae

Irregular (quasi)varieties of groupoids are (quasi)varieties that do not contain semilattices. The regularization of a (strongly) irregular variety 𝒱 of groupoids is the smallest variety containing 𝒱 and the variety 𝒮 of semilattices. Its quasiregularization is the smallest quasivariety containing 𝒱 and 𝒮 . In an earlier paper the authors described the lattice of quasivarieties of cancellative commutative binary modes, i.e. idempotent commutative and entropic (or medial) groupoids. They are all irregular...

Some remarks on simple Bol loops

Gábor P. Nagy (2008)

Commentationes Mathematicae Universitatis Carolinae

In this paper we make some remarks on simple Bol loops which were motivated by questions at the LOOPS'07 conference. We also list some open problems on simple loops.

Some results in bipolar-valued fuzzy ordered AG-groupoids

Faisal, Naveed Yaqoob, Arsham Borumand Saeid (2012)

Discussiones Mathematicae - General Algebra and Applications

In this paper, we introduce the concept of bipolar-valued fuzzification of ordered 𝓐𝓖-groupoids and discuss some structural properties of bipolar-valued fuzzy two-sided ideals of an intra-regular ordered 𝓐𝓖-groupoid.

Split extensions and semidirect products of unitary magmas

Marino Gran, George Janelidze, Manuela Sobral (2019)

Commentationes Mathematicae Universitatis Carolinae

We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivalence between the categories of split extensions and of (suitably defined) actions of unitary magmas on unitary magmas. The class of split extensions is pullback stable but not closed under composition. We introduce two subclasses of it that have both of these properties.

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