(–1, 1) metabelian rings
DOI:
https://doi.org/10.5269/bspm.v35i2.26250Resumen
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.
Referencias
1. Albert, A. A., Almost alternative algebras, Portug. Math. J., 8, 23-36, (1949).
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).
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).
Descargas
Publicado
2016-03-20
Número
Sección
Research Articles
Licencia
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
