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On Semiprime Finitely Generated Right Alternative Weakly M-Rings
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On Semiprime Finitely Generated Right Alternative Weakly M-Rings

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Abstract:

Right alternative rings, satisfying the weakly M-ring identity (w,xy,z) = x(w,y,z) are studied. Any one of the following additional assumptions imply associativity: semi prime and a finite number of generators: prime with char. ≠ 2 and minimum condition on either right ideals or on trivial left ideals, or simple and char. ≠ 2.

Info:

Periodical:
The Bulletin of Society for Mathematical Services and Standards (Volume 6)
Pages:
9-12
DOI:
https://doi.org/10.18052/www.scipress.com/BSMaSS.6.9
Citation:
K. Jayalakshmi and C. Manjula, "On Semiprime Finitely Generated Right Alternative Weakly M-Rings", The Bulletin of Society for Mathematical Services and Standards, Vol. 6, pp. 9-12, 2013
Online since:
June 2013
Authors:
K. Jayalakshmi, C. Manjula
Keywords:
Center, Middle Nucleus, M-Ring, Nucleus, Prime Ring, Right Alternative
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Distribution:
Open Access

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This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

A. Thedy, Right alternative rings, J. Algebra 37 (1975), 1-43.

I.R. Hentzel, Nil-semi-simple locally (-1, 1) rings, Bull. Iranian Math. Soc. 9 (1981), 11-14.

I.R. Hentzel and H.F. Smith, Semi prime locally (-1, 1) rings with minimal condition, Algs Gps. And Geoms. 2 (1985), 26-52.

I.R. Hentzel and H.F. Smith, Simple locally (-1, 1) nil rings, J. Algebra 101 (1986), 262-272.

K.A. Zhevlakov, A.M. Slinko, I.P. Shestakov and A.I. Shirshov, Rings that are nearly associative, Academic press (1982).

V.G. Skosyrskii, Right alternative algebras with minimality condition for right ideals (Russian), Algebra I Logika 24 (1985), 205-210.

V.G. Skosyrskii, Right alternative algebras (Russian), Algebra I Logika 23 (1984), 185-192.

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