Derivation alternator rings with S(a, b, c)=0
DOI :
https://doi.org/10.5269/bspm.64969Résumé
In this paper, we discuss the derivation alternator rings which are nonassociative but not (-1.1) rings. By assuming some additional conditions, we prove that derivation alternator rings are (-1,1) rings. Here we validate a semiprime derivation alternator ring with commutators in the left nucleus satisfies the identity . By using this we show that a semiprime derivation alternator ring with commutators in the left nucleus is a (-1,1) ring.
Références
1. Hentzel, I. R., Kleinfeld, E. and Smith, H. F. “On rings in the join of associative and commutative”, J. Algebra, Vol. 149, No. 2 (1992), 528-537.
2. Hentzel, I. R. “The characterization of (-1,1) rings” J. Algebra 30(1974),236-258.
3. Hentzel. I. R., Hogben, L. and Smith H. F. “Flexible derivation alternator rings”, Com. in. algebra, 8 (20) (1980), 1997-2014.
4. Kleinfeld, E. “Rings with (x,y,x) and commutators in the left nucleus”, Comm. in. Algebra, 16 (10), (1988), 2023-2029.
5. Kleinfeld, E. “Generalization of alternative rings I”, J. Algebra, 18 (1971), 304-325.
6. Thedy, A. “On rings with commutators in the nucleus”, Math. Z. 119 (1971), 213-218.
2. Hentzel, I. R. “The characterization of (-1,1) rings” J. Algebra 30(1974),236-258.
3. Hentzel. I. R., Hogben, L. and Smith H. F. “Flexible derivation alternator rings”, Com. in. algebra, 8 (20) (1980), 1997-2014.
4. Kleinfeld, E. “Rings with (x,y,x) and commutators in the left nucleus”, Comm. in. Algebra, 16 (10), (1988), 2023-2029.
5. Kleinfeld, E. “Generalization of alternative rings I”, J. Algebra, 18 (1971), 304-325.
6. Thedy, A. “On rings with commutators in the nucleus”, Math. Z. 119 (1971), 213-218.
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Publié
2024-05-03
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Research Articles
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