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Solution of distributive-like quasigroup functional equations

Fedir M. Sokhatsky, Halyna V. Krainichuk (2012)

Commentationes Mathematicae Universitatis Carolinae

We are investigating quasigroup functional equation classification up to parastrophic equivalence [Sokhatsky F.M.: On classification of functional equations on quasigroups, Ukrainian Math. J. 56 (2004), no. 4, 1259–1266 (in Ukrainian)]. If functional equations are parastrophically equivalent, then their functional variables can be renamed in such a way that the obtained equations are equivalent, i.e., their solution sets are equal. There exist five classes of generalized distributive-like quasigroup...

Some distributivities in GBbi-QRs characterizing Boolean rings

Joanna Kaleta (2004)

Discussiones Mathematicae - General Algebra and Applications

This paper presents some manner of characterization of Boolean rings. These algebraic systems one can also characterize by means of some distributivities satisfied in GBbi-QRs.

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.

Subloops of sedenions

Benard M. Kivunge, Jonathan D. H Smith (2004)

Commentationes Mathematicae Universitatis Carolinae

This note investigates sedenion multiplication from the standpoint of loop theory. New two-sided loops are obtained within the version of the sedenions introduced by the second author. Conditions are given for the satisfaction of standard loop-theoretical identities within these loops.

Symmetries in hexagonal quasigroups

Vladimír Volenec, Mea Bombardelli (2007)

Archivum Mathematicum

Hexagonal quasigroup is idempotent, medial and semisymmetric quasigroup. In this article we define and study symmetries about a point, segment and ordered triple of points in hexagonal quasigroups. The main results are the theorems on composition of two and three symmetries.

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