On quasivarieties of nilpotent Moufang loops. I

Vasile I. Ursu

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 3, page 475-489
  • ISSN: 0010-2628

Abstract

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In this part the smallest non-abelian quasivarieties for nilpotent Moufang loops are described.

How to cite

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Ursu, Vasile I.. "On quasivarieties of nilpotent Moufang loops. I." Commentationes Mathematicae Universitatis Carolinae 53.3 (2012): 475-489. <http://eudml.org/doc/247019>.

@article{Ursu2012,
abstract = {In this part the smallest non-abelian quasivarieties for nilpotent Moufang loops are described.},
author = {Ursu, Vasile I.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; associator; commutator; nilpotent; quasivarieties; quasiidentities; identities; quasivarieties of nilpotent Moufang loops; free Moufang loops; varieties of loops; associators; commutators; quasiidentities},
language = {eng},
number = {3},
pages = {475-489},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On quasivarieties of nilpotent Moufang loops. I},
url = {http://eudml.org/doc/247019},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Ursu, Vasile I.
TI - On quasivarieties of nilpotent Moufang loops. I
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 3
SP - 475
EP - 489
AB - In this part the smallest non-abelian quasivarieties for nilpotent Moufang loops are described.
LA - eng
KW - loop; associator; commutator; nilpotent; quasivarieties; quasiidentities; identities; quasivarieties of nilpotent Moufang loops; free Moufang loops; varieties of loops; associators; commutators; quasiidentities
UR - http://eudml.org/doc/247019
ER -

References

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  1. Mal'cev A.I., On the inclusion of associative systems in groups, I., Mat. Sbornik 6 (1939), no. 2, 331–336. MR0002152
  2. Mal'cev A.I., On the inclusion of associative systems in groups, II., Mat. Sbornik 8 (1940), no. 2, 251–263. MR0003420
  3. Mal'cev A.I., Quasiprimitive classes of abstract algebras, Dokl. Akad. Nauk SSSR (N.S.) 108 (1956), 187–189. MR0079572
  4. Mal'cev A.I., Several remarks on quasivarieties of algebraic systems, Algebra i Logika Sem. 5 (1966), no. 3, 3–9. MR0205902
  5. Mal'cev A. I., Some borderline problems of algebra and logic, 1968 Proc. Internat. Congr. Math. (Moscow, 1966), pp. 217–231. MR0233751
  6. Mal'cev A.I., Algebraic Systems, Moscow, Nauka, 1970. Zbl0223.08001MR0282908
  7. Ursu V.I., On identities of nilpotent Moufang loops, Rev. Roumaine Math. Pures Appl. 45 (2000), no. 3, 537–548. Zbl0993.20043MR1840173
  8. Bruck R.H., A Survey of Binary Systems, Springer, Berlin-Heidelberg-New York, 1958. Zbl0141.01401MR0093552
  9. Koval'ski A.V., Ursu V.I., An equational theory for a nilpotent A-loop, Algebra Logika 49 (2010), no. 4, 479–497. MR2790173
  10. Kargapolov M.I., Merzlyakov Yu.I., Fundamentals of Group Theory, Moscow, Nauka, 1982. Zbl0884.20001MR0677282

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