Some regular quasivarieties of commutative binary modes
K. Matczak; Anna B. Romanowska
Commentationes Mathematicae Universitatis Carolinae (2014)
- Volume: 55, Issue: 4, page 471-484
- ISSN: 0010-2628
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topMatczak, K., and Romanowska, Anna B.. "Some regular quasivarieties of commutative binary modes." Commentationes Mathematicae Universitatis Carolinae 55.4 (2014): 471-484. <http://eudml.org/doc/262024>.
@article{Matczak2014,
abstract = {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.},
author = {Matczak, K., Romanowska, Anna B.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {regular quasivarieties; regular quasi-identity; modes; affine spaces; commutative binary modes; regular quasivarieties; regular quasi-identities; affine spaces; commutative binary modes; commutative idempotent medial groupoids; lattices of quasivarieties; quasi-regularizations; irregular varieties; lattices of varieties},
language = {eng},
number = {4},
pages = {471-484},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some regular quasivarieties of commutative binary modes},
url = {http://eudml.org/doc/262024},
volume = {55},
year = {2014},
}
TY - JOUR
AU - Matczak, K.
AU - Romanowska, Anna B.
TI - Some regular quasivarieties of commutative binary modes
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 4
SP - 471
EP - 484
AB - 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.
LA - eng
KW - regular quasivarieties; regular quasi-identity; modes; affine spaces; commutative binary modes; regular quasivarieties; regular quasi-identities; affine spaces; commutative binary modes; commutative idempotent medial groupoids; lattices of quasivarieties; quasi-regularizations; irregular varieties; lattices of varieties
UR - http://eudml.org/doc/262024
ER -
References
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