Antiflexible Rings with Commutators in the Left Nucleus

M.Hema Prasad*, D. Bharathi**
* Assistant Professor in Mathematics, Department of Science & Humanities, SITAMS, Chittoor, A.P. India.
** Associate Professor in Mathematics, Department of Mathematics, S.V. University, Tirupati, A.P. India.
Periodicity:October - December'2014
DOI : https://doi.org/10.26634/jmat.3.4.3188

Abstract

In this paper, the authors have assumed that 'R' is an antiflexible ring with commutators and (a, b, c) in the left nucleus. Using this, they have proved that the commutators are in the middle of the nucleus. Next they have proved that an antiflexible ring R cannot be simple. They assumed T = {t∈ Nl / t (R, R, R) = 0}and proved that T is an ideal of R and T (R, R, R)= 0 and then they have proved that T∩A = 0, ((a, b, a), R) = 0. Finally using these results they conclude that, if R is a prime antiflexible ring of characteristic ≠ 3, then R is associative.

Keywords

Antiflexible rings, commutator, left nucleus, associative, prime ring.

How to Cite this Article?

Prasad, M.H., and Bharathi, D. (2014). Antiflexible Rings with Commutators in the Left Nucleus. i-manager’s Journal on Mathematics, 3(4), 51-56. https://doi.org/10.26634/jmat.3.4.3188

References

[1]. A. A. Albert. (1948). “Power Associative Rings”, Trans. Amer. Math. Soc., Vol.64, pp.552-593.
[2]. C.T. Anderson and D. L. Outcalt. (1968). “On Simple Antiflexible Rings”, J. Algebra, Vol.10, pp.310 - 320.
[3]. A. Thedy. (1971). “On Rings satisfying ((a, b, c), d) = 0”, Proc. Amer. Math. Soc., Vol.29, pp.250–254.
[4]. A. Thedy. (1971). “On rings with commutators in nuclei”, Math. Z., Vol.119, pp.213 - 218.
[5]. A. H. Boers. (1971). “The nucleus in the associative ring”, Proc. Kon. Ned. Akad. Vanwet. Vol 74 et Indag. Math. 33, pp.464 - 470.
[6]. H. A. Celik. (1972). “On primitive and prime Antiflexible Rings”, Journal of Algebra, Vol.20, pp.428 - 440.
[7]. A. Thedy. (1975). “Right alternative rings”, Journal of Algebra, Vol.37, pp.1 - 43.
[8]. M. Mahivee. (1975). “On prime right alternative rings”, (Russian) Algebra I logika Vol.14, pp.56 - 60.
[9]. H.A. Celik and D. L. Outcalt. (1975). “Power – Associativity of Antiflexible rings”, Proceedings of the American Mathematical Society, Vol.53(1), pp.19 - 23.
[10]. E. Kleinfeld. (1988). “Rings with (x, y, x) and commutators in the left nucleus”, Comm. Algebra, Vol.16, pp.2023-2029.
[11]. Y. Paul. (1990). “Prime rings satisfying (x, y, z) = (x, z, y)”, Proc. Symposium of Algebra and Number Theory, Kochi, Kerala, India, pp.91-95.
[12]. Kosier. F, (1962). “On a class of nonflexible algebras”. Trans. Am. Math. Soc. Vol.102, pp.299-318.
[13]. Kleinfeld, E (1957). “Assosymmetric rings”, Proc. Amer. Math. Soc., Vol. 8, pp.983-986.
If you have access to this article please login to view the article or kindly login to purchase the article

Purchase Instant Access

Single Article

North Americas,UK,
Middle East,Europe
India Rest of world
USD EUR INR USD-ROW
Pdf 35 35 200 20
Online 35 35 200 15
Pdf & Online 35 35 400 25

Options for accessing this content:
  • If you would like institutional access to this content, please recommend the title to your librarian.
    Library Recommendation Form
  • If you already have i-manager's user account: Login above and proceed to purchase the article.
  • New Users: Please register, then proceed to purchase the article.