Some regular quasivarieties of commutative binary modes

Commentationes mathematicae Universitatis Carolinae

K. Matczak¹ 

关键词: regular quasivarieties;    regular quasi-identity;    modes;    affine spaces;    commutative binary modes;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

Irregular (quasi)varieties of groupoids are (quasi)varieties that do not contain semilattices. The regularization of a (strongly) irregular variety $\mathcal{V}$ of groupoids is the smallest variety containing $\mathcal{V}$ and the variety $\mathcal{S}$ of semilattices. Its quasiregularization is the smallest quasivariety containing $\mathcal{V}$ and $\mathcal{S}$. 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 and the lattice contains all irregular varieties of such groupoids. This paper extends the earlier result, by investigating some regular quasivarieties. It provides a full description of the lattice of subquasivarieties of the regularization of any irregular variety of commutative binary modes.

【 授权许可】

CC BY