Special Issue for Papers from the Conference in Honor of the 80th Birthday of Professor Boris I. PlotkinNo Access

THE FREE ALTERNATIVE SUPERALGEBRA ON ONE ODD GENERATOR

IVAN SHESTAKOV

Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, Brasil

Sobolev Institute of Mathematics, Novosibirsk, Russia

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and

NATALIA ZHUKAVETS

Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic

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https://doi.org/10.1142/S0218196707003895Cited by:15 (Source: Crossref)

Abstract

A base of the free alternative superalgebra on one odd generator is constructed. As a corollary, a base of the alternative Grassmann algebra is given. We also find a new element of degree 5 from the radical of the free alternative algebra of countable rank.

For Professor B. I. Plotkin in honor of his 80th birthday

Keywords:

AMSC: 17D05, 17A50, 17A70

References

V. T. Filippov, V. K. Kharchenko and I. P. Shestakov (eds.), Dniester Notebook: Unsolved Problems in the Theory of Rings and Modules, 4th edn. (Institute of Mathematics, Novosibirsk, 1993). Google Scholar
G. V. Dorofeev, Sibirsk. Mat. Zh. 4, 1049 (1963). Google Scholar
A. V. Il'tyakov, Algebra Logika 23(2), 136 (1984). Google Scholar
E. N. Kuz'min and I. P. Shestakov, Nonassociative structures, VINITI, Itogi nauki i tekhniki, seria, Fundamental Branches 57 (Moscow, 1990) pp. 179–266. Google Scholar
S. V. Pchelintsev, Sibirsk. Mat. Zh. 32(6), 142 (1991). Google Scholar
M. L. Racine, J. Algebra 115, 251 (1988), DOI: 10.1016/0021-8693(88)90294-3. Crossref, Web of Science, Google Scholar
I. P. Shestakov, Algebra Logika 14(3), 354 (1975). Google Scholar
I. P. Shestakov, Mat. Sb. (N. S.) 122(164), 31 (1983). Google Scholar
I. P. Shestakov, Siberian Adv. Math. 9(2), 83 (1999). Google Scholar
I. P. Shestakov, J. Algebra Appl. 2(4), 451 (2003), DOI: 10.1142/S021949880300060X. Link, Web of Science, Google Scholar
I. Shestakov and N. Zhukavets, Comm. Algebra 34(4), 1319 (2006), DOI: 10.1080/00927870500454570. Crossref, Web of Science, Google Scholar
I. Shestakov and N. Zhukavets, J. Algebra Appl. 5(4), 521 (2006), DOI: 10.1142/S0219498806001867. Link, Web of Science, Google Scholar
I. Shestakov and N. Zhukavets, J. Algebra 301(2), 587 (2006), DOI: 10.1016/j.jalgebra.2005.11.003. Crossref, Web of Science, Google Scholar
A. I. Shirshov, Mat. Sb. 45(87), 113 (1958). Google Scholar
A. I. Shirshov, Algebra Logika 1(1), 14 (1962). Google Scholar
A. I. Shirshov, Sibirsk. Mat. Zh. 3, 132 (1962). Google Scholar
M. Vaughan-Lee, Internat. J. Algebra Comput. 8(1), 97 (1998), DOI: 10.1142/S0218196798000065. Link, Web of Science, Google Scholar
E. I. Zelmanov and I. P. Shestakov, Izv. Akad. Nauk SSSR, Ser. Mat. 54(4), 676 (1990). Google Scholar
K. A. Zhevlakov et al. , Rings That are Nearly Associative ( Nauka , Moscow , 1978 ) . Google Scholar
N. Zhukavets and I. Shestakov, Fundam. Prikl. Mat. 10(4), 97 (2004). Google Scholar
V. T. Filippov, Groups and Other Algebraic Systems with Chain Conditions (Nauka, Novosibirsk, 1984) pp. 139–156. Google Scholar