Units in quasigroups with classical Bol--Moufang type identities

Natalia Didurik; Viktor Alekseevich Shcherbakov

Commentationes Mathematicae Universitatis Carolinae (2020)

  • Volume: 61, Issue: 4, page 427-435
  • ISSN: 0010-2628

Abstract

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We proceed with Kunen's research about existence of units (left, right, two-sided) in quasigroups with classical Bol--Moufang type identities, listed in paper Extra loops II, by F. Fenyves (1969). We consider those Bol--Moufang identities where it has not been decided yet whether a quasigroup fulfilling this identity has to possess a left or right identity. We also provide a table of all Moufang--Bol identities, indicating at each whether it describes the variety of groups, and whether it forces out the left unit or the right unit.

How to cite

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Didurik, Natalia, and Shcherbakov, Viktor Alekseevich. "Units in quasigroups with classical Bol--Moufang type identities." Commentationes Mathematicae Universitatis Carolinae 61.4 (2020): 427-435. <http://eudml.org/doc/296956>.

@article{Didurik2020,
abstract = {We proceed with Kunen's research about existence of units (left, right, two-sided) in quasigroups with classical Bol--Moufang type identities, listed in paper Extra loops II, by F. Fenyves (1969). We consider those Bol--Moufang identities where it has not been decided yet whether a quasigroup fulfilling this identity has to possess a left or right identity. We also provide a table of all Moufang--Bol identities, indicating at each whether it describes the variety of groups, and whether it forces out the left unit or the right unit.},
author = {Didurik, Natalia, Shcherbakov, Viktor Alekseevich},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasigroup; Bol--Moufang type identity; right unit; left unit},
language = {eng},
number = {4},
pages = {427-435},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Units in quasigroups with classical Bol--Moufang type identities},
url = {http://eudml.org/doc/296956},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Didurik, Natalia
AU - Shcherbakov, Viktor Alekseevich
TI - Units in quasigroups with classical Bol--Moufang type identities
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 4
SP - 427
EP - 435
AB - We proceed with Kunen's research about existence of units (left, right, two-sided) in quasigroups with classical Bol--Moufang type identities, listed in paper Extra loops II, by F. Fenyves (1969). We consider those Bol--Moufang identities where it has not been decided yet whether a quasigroup fulfilling this identity has to possess a left or right identity. We also provide a table of all Moufang--Bol identities, indicating at each whether it describes the variety of groups, and whether it forces out the left unit or the right unit.
LA - eng
KW - quasigroup; Bol--Moufang type identity; right unit; left unit
UR - http://eudml.org/doc/296956
ER -

References

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