2001, VOLUME 7, NUMBER 3, PAGES 849-871

The structure of weak identities on the Grassman envelopes of central-metabelian alternative superalgebras of superrank 1 over a field of characteristic 3

S. V. Pchelintsev


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The work is devoted to clarify the structure of weak identities of central-metabelian alternative Grassmann algebras over a field of characteristic 3. Canonical systems of weak identities {fn} and {gn} are constructed:

fn := [[x1, x2], x3] R(x4) ... R(xn-2) [xn-1, xn],    n = 4k+2, 4k+3;
gn := [x1, x2]R(x3) ... R(xn-2) [xn-1, xn],   n = 4k, 4k+3.

It is proved that for any infinitie system of nonzero weak identity there is number n0, since which each of identities of the given system of a degree n > n0 is equivalent to one of canonical identities fn or gn.

As consequence the variety of alternative algebras with unit over a field of characteristic 3 which has not final bases of identities is specified.

It is proved also, that the class of weak identities of a rather high degree coinside with the class of mufang functions.

All articles are published in Russian.

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Last modified: December 23, 2001