(–1, 1) metabelian rings
DOI:
https://doi.org/10.5269/bspm.v35i2.26250Abstract
The structure of the set of all non- nilpotent (–1, 1) metabelian rings is studied. An additive basis of a free (–1, 1) metabelian ring is constructed. It is proved that any identity in a non- nilpotent 2, 3-torsion free (–1, 1) metabelian ring of degree greater than or equal to 6 is a consequence four defining identities of m where m is the metabelian (–1, 1) ring.
References
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2. Nikitin, A. A., Almost alternative algebras, Algebra i logica [Algebra and Logic], 13 No.5, 501-533, (1974).
3. Il’tyakov, A. v., The lattice of sub varieties of the variety of two-step solvable alternative algebras, Algebra i logica [Algebra and Logic], 21, No. 2, 170-177, (1982).
4. Dorofeev, G. V., An example of a solvable but not nilpotent alternative ring, Uspekhi Mat. Nauk [Russian Math. Surveys], 15, No. 3, 147-150, (1960).
5. Zhevlakov, K. A., Slin’ko, A. M., Shestakov, I.P. and Shirshov, A.I. Rings that are nearly Associative, Academic, New York, (1982); Nauka, (1978).
6. Pchelintsev, S. V., Varieties of solvable of index-2 alternative algebras over the field of characteristic 3, Mat. Zametki [Math. Note], 66, No. 4, 556-566, (1999).
7. Pchelintsev, S. V. Varieties of solvable of index 2, Mat. Sb. [Math. USSR ? Sb.], 115, No. 2 179-203, (1981).
8. Belkin,. V. P., On varieties of right alternative algebras, Algebra i logica [Algebra and Logic], 15, No. 5 491-508, (1976).
9. Medvevdev. Yu. A., Finite Basability of varieties with two-term identies, Algebra i logika [Algebra and Logic], 17, No. 6, 705-726, (1978).
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2016-03-20
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