ABOUT STRICTLY SIMPLE TERNARY ALGEBRAS WITH OPERATORS
https://doi.org/10.22405/2226-8383-2013-14-4-197-204
Abstract
In this work is given some conditions of strictly simplicity for algebras with operators having one ternary main operation. It is described strictly simple unars with standard and symmetric Mal’tsev operations and with standard majority operation. The description of simple unars with standard majority operation is obtained as well.
About the Author
V. L. Usol’tsevRussian Federation
References
1. Szendrei A. Simple surjective algebras having no proper subalgebras ´ . // J. Austral. Math. Soc. Ser A, 1990. №. 48. P. 329–346.
2. Szendrei A. A survey on strictly simple algebras and minimal varietie ´ s. //Univ. Algebra and Quasigroup Theory. Research and Exposition in Math., 1992, Vol. 19. P. 209–239.
3. Kearnes K.A., Szendrei A. A characterization of minimal locally finite varieties. ´ // Trans. Amer. Math. Soc., 1997. Vol. 349, № 5. P. 1749–1768.
4. Kearnes K.A., Szendrei A. Projectivity and isomorphism of strictly simple ´ algebras. // Algebra Universalis, 1998. Vol. 39. P.45–56.
5. Bulatov A., Krokhin A., Jeavons P. Classifying the Complexity of Constraints using Finite Algebras. // SIAM J. Comput., 2005, Vol. 34, № 3. P.720–752.
6. McKenzie R., Freese R. Commutator theory for congruence modular varieties. // London Math. Soc. Lecture Notes Ser., 1987. Vol. 125, 227 p. 6. Valeriot M. Finite simple Abelian algebras are strictly simple. //Proc. of the Amer. Math. Soc., 1990. № 108. P.49–57.
7. Artamonov V. A. Polinomial’no polnye algebry [Polynomially complete algebras]. // Uch. zap. Orlovskogo gos. un-ta, 2012. Vol. 6(50), part 2. P. 23–29 (in Russian).
8. Mar´oti M., McKenzie R. Existence theorems for weakly symmetric operations. // Algebra Universalis, 2008. Vol. 59, |No. 3-4. P. 463–489.
9. Markovi´c P., McKenzie R. Few subpowers, congruence distributivity and nearunanimity terms. Algebra Universalis, 2008. Vol. 58. P. 119–128.
10. Usol’tsev V.L. Simple and pseudosimple algebras with operators. //J. of Mathematical Sciences [Fund. i Prikl. Matem.], 2010. Vol. 164, |No. 2. P. 281–293. DOI: 10.1007/S1095800997306.
11. Kartashov V. K. Ob unarakh s mal’tsevskoi operatsiei [About unars with Mal’tsev operation]. // Univ. algebra i ee prilozheniia: Tez. dokl. mezhdunar. sem. Volgograd, 1999. P. 31–32 (in Russian).
12. Usol’tsev V. L. Svobodnye algebry mnogoobraziia unarov s mal’tsevskoi operatsiei p, zadannogo tozhdestvom p(x, y, x) = y [Free algebras of variety of unars with Mal’tsev operation, set by identity p(x, y, x) = y]. // Chebyshevsky sb., 2011. Vol. 12, № 2(38). P. 127–134 (in Russian).
13. Usol’tsev V. L. O polinomial’no polnykh i abelevykh unarakh s mal’tsevskoi operatsiei [About polynomially complete and Abelian unars with Mal’tsev operation]. // Uch. zap. Orlovskogo gos. un-ta, 2012. Vol. 6(50), part 2. P. 229– 236 (in Russian).
Review
For citations:
Usol’tsev V.L. ABOUT STRICTLY SIMPLE TERNARY ALGEBRAS WITH OPERATORS. Chebyshevskii Sbornik. 2013;14(4):197-204. (In Russ.) https://doi.org/10.22405/2226-8383-2013-14-4-197-204