Identities of the Model Algebra of Multiplicity 2
- 5 Downloads
We construct an additive basis of the free algebra of the variety generated by the model algebra of multiplicity 2 over an infinite field of characteristic not 2 and 3. Using the basis we remove a restriction on the characteristic in the theorem on identities of the model algebra (previously the same was proved in the case of characteristic 0). In particular, we prove that the kernel of the relatively free Lie-nilpotent algebra of index 5 coincides with the ideal of identities of the model algebra of multiplicity 2.
Keywordsfree algebra proper polynomial identity of Lie-nilpotency additive basis identities of a model algebra
Unable to display preview. Download preview PDF.
- 2.Latyshev V. N., “Finite generation of a T-ideal with the element [x1, x2, x3, x4],” Sib. Mat. Zh., vol. 6, No. 6, 1432–1434 (1965).Google Scholar
- 4.Volichenko I. B., T-Ideal Generated by the Element [x1, x2, x3, x4] [Russian] [Preprint, no. 22], Inst. Mat. Akad. Nauk BSSR, Minsk (1978).Google Scholar
- 5.Grishin A. V., “An infinitely based T-ideal over a field of characteristic 2,” in: Abstracts: The International Conference on Algebra and Analysis Dedicated to N. G. Chebotarev on the Occasion of His 100 Birthday, Kazan, 5–11 June 1994, Kazan, 1994, 29.Google Scholar
- 11.Pchelintsev S. V., “Relatively free associative algebras of ranks 2 and 3 with Lie nilpotency identity and systems of generators of some T-spaces,” arXiv:1801.07771.Google Scholar
- 13.Zhevlakov K. A., Slinko A. M., Shestakov I. P., and Shirshov A. I., Rings That Are Nearly Associative, Academic Press, New York (1982).Google Scholar
- 15.Buchnev A. A., Filippov V. T., and Shestakov I. P., “Checking identities of nonassociative algebras by computer,” in: III Siberian Congress on Applied and Industrial Mathematics (IN-PRIM-98), Izdat. Inst. Mat., Novosibirsk, 1998, 9.Google Scholar