On commutativity of right S-unital rings with some polynomial constraints

Authors

  • H. A. S. Abujabal King Abdulaziz University.
  • M. A. Khan King Abdulaziz University.

DOI:

https://doi.org/10.22199/S07160917.1995.0002.00003

Abstract

We study the commutativity of certain class of rings, namely rings with unity 1 and right s-unital under each of the following properties [yxm - xn f (y) xP, x]= 0, [yxm + xn f (y) xP, x] = 0, where f (t) is a polynomial in t2Z [t] varying with pair of ring elements x, y and m, n, p are fixed non-negative integers. Moreover, the results have been extended to the case when m and n depend on the choice of x and y and the ring satisfies the Chacron's Theorem.

Author Biographies

H. A. S. Abujabal, King Abdulaziz University.

Department of Mathematics,
Faculty of Science.

M. A. Khan, King Abdulaziz University.

Department of Mathematics,
Faculty of Science.

References

[1] H. A. Abujabal and M. S. Khan : "On Commutativity Theorern for Rings", Internat. J. Math. and Math. Sci., 13, pp. 87- 92, (1990).
[2] H. A. S. Abujabal : "Sorne Cornrnutativity Results for Rings", Beitriige Zur Alg. und Geo., 32, pp . 141- 151, (1991).
[3] H. A. S. Abujabal and M. A. Khan : "On Commutativity of One-sided S-unital Rings", Internat J. Math. and Math. Sci., 15, pp. 813-818, (1992).
[4] H. A. S. Abujabal ; M. A. Khan and M. S. Samman : "On Coinmutativity of One Sided S-unital Rings", Tamkang J. Math., 23, pp. 253- 267, (1992).
[5] H. A. S. Abujabal "Two Cornrnutativity Results for Rings", Math. Japon, 38, pp. 297- 299, (1993).
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[7] M. Ashraf ; M. A. Quadri and V. Jacob, "Cornrnutativity of Right S-unital Rings Under Sorne Polynornial Constraints", Tamkang J. Math., 24, pp. 23- 28, (1993).
[8] l. N. Herstein : " Two Rernarks on the Cornrnutativity of Rings", Cand. J. Math., 7, pp. 411-412, (1995).
[9] Y. Hirano ; Y. Kobayashi and H. Tominaga : "Sorne Polynomial ldentities and Commutativity of S-unital Rings", Math. J. Okayama Univ., 24, pp. 7- 13, (1982).
[10] H. Komatsu and H. Tominaga : "Chacron's Condition and Commutativity Theorems", Math. J. Okayama Univ., 31, pp. 101 - 120, (1989).
[11] H. Komatsu ; T. Nishinaka and H. Tominaga : "On Commutativity of Rings", Rad. Mat., 6, pp. 303- 311, (1990).
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[13] W. Streb: "Zur Struktur Nichtommutativer Ringe", Math. J. Okayama Univ., 31, pp. 135- 140, (1989).

Published

2018-04-03

How to Cite

[1]
H. A. S. Abujabal and M. A. Khan, “On commutativity of right S-unital rings with some polynomial constraints”, Proyecciones (Antofagasta, On line), vol. 14, no. 2, pp. 89-96, Apr. 2018.

Issue

Section

Artículos