| Author(s): |
Sverchkov, S. R.
[1]
Total Authors: 1
|
| Affiliation: | [1] Novosibirsk State Univ, Novosibirsk 630090 - Russia
Total Affiliations: 1
|
| Document type: | Journal article |
| Source: | Algebra and Logic; v. 50, n. 1, p. 62-88, MAR 2011. |
| Web of Science Citations: | 1 |
| Abstract | |
Let J{[}X(n)], SJ{[}X(n)], and As{[}X(n)] be a free Jordan algebra, a free special Jordan algebra, and a free associative algebra on a set of generators X(n) = [x(1), x(2), ..., x(n)] and S(n) be the kernel of a canonical homomorphism pi : J{[}Xn] -> SJ{[}X(n)]. Nonzero elements in Sn are called s-identities. The Shirshov-McDonald theorem (see {[}1]) states that if f(x(1), x(2), x(3)) is an element of S(3) and d(x3) (f) <= 1 then f = 0. In particular, S(2) = (0). In {[}2], it was proved that S(3) not equal (0). In {[}3], s-identities G(8), G(9). S(3) of degrees 8 and 9 were constructed based on the proof in {[}2]. Currently we know of just a few examples of s-identities (see {[}3-7]). In the present paper we prove that all Jordan s-identities in three variables are consequences of the Glennie s-identity G(8) of degree 8, which solves K. A. Zhevlakov's problem (see {[}8, Problem 1.40]). All algebras are treated over a field F of characteristic 0. For standard definitions and notation, we ask the reader to consult {[}1]. (AU) | |
| FAPESP's process: | 10/50171-8 - Sergei Sverchkov | Siberian Branch of the Russian Academy of Agricultural Sciences - Rússia |
| Grantee: | Ivan Chestakov |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |