Antiflexible Rings with Weak Novikov Identity

M. Hema Prasad; Dr. D. Bharathi

doi:https://doi.org/10.14445/22315373/IJMTT-V14P514

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 14 | Number 2 | Year 2014 | Article Id. IJMTT-V14P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V14P514

Antiflexible Rings with Weak Novikov Identity

M. Hema Prasad , Dr. D. Bharathi

Abstract

If R is an antiflexible ring of characteristic ≠ 2, 3 with Weak Novikov identity (w, x, y z) = y (w, x, z) then Strong Novikov identity x (y z) = y(x z). Using this results we prove that, if R is a prime not associative antiflexible ring of characteristic ≠ 2, 3 satisying the Weak Novikov identity (w, x, yz) = y (w, x, z) then R is either an alternative ring (or) strongly (-1,1) ring.

Keywords

Antiflexible rings, Weak Novikov identity, Strong Novikov identity, alternative ring, strongly (-1, 1) ring.

References

[1] E. Kleinfeld and H. F. Smith, “A generalization of Novikov rings, Non-Associative Algebra and its applications”, kluwer Academic publishers (1994), 219-222.
[2] E. Kleinfeld and M. Kleinfeld, “Variations of the Novikov Identities”, Communications in Algebra, 24(5),1996,1707-1711.
[3] M. Kleinfeld, “Rings with x(yz) = y(xz)”, Communications in Algebra, 23(13),1995, 5085-5093.
[4] K. Subhashini and P. Vijasekhara Reddy, “Weak Novikov Identity in the join of (-1, 1) Rings”, International Journal of Algebra, vol.6, 2012, no.30,1457-1461.
[5] M. Hema Prasad, Dr. D. Bharathi, Dr. M. Munirathnam, “Simple Antiflexible rings”, International Journal of Scientific & Engineering Research, Volume 5, Issue 3, March-2014, 1286-1288.

Citation :

M. Hema Prasad , Dr. D. Bharathi, "Antiflexible Rings with Weak Novikov Identity," International Journal of Mathematics Trends and Technology (IJMTT), vol. 14, no. 2, pp. 88-92, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V14P514