Volume 4, Issue 1, February 2018, Page: 13-19
On Commutativity of Rings Under Certain Polynomial Constraints
Mohammad Shadab Khan, Department of Commerce, Aligarh Muslim University, Aligarh, India
Received: Jan. 9, 2018;       Accepted: Feb. 27, 2018;       Published: Mar. 19, 2018
DOI: 10.11648/j.ijdsa.20180401.13      View  1216      Downloads  57
The pioneer theorem of Weddernburn on commutativity of division rings was proved in the very beginning of twentieth century. Aside from its own intrinsic beauty and important role in many diverse parts of algebra specially, the theorem serves as the starting point for investigations of certain kinds of conditions that render a ring commutative. A large part of the results in this area was developed in the hands of many distinguished mathematicians like Jacobson, Herstein, Kaplansky, Faith, Martindale, Nakayama, Bell and many others. The purpose of the present paper is to investigate commutativity of a ring with unity 1 satisfying certain polynomial constraints. The main result of the first section asserts that a ring is commutative if at least one of the integral exponent used in the polynomial constraints of the theorem is zero and the ring also satisfies the property Q(n) Further, in the second section, commutativity of a ring with unity 1 has also been established under a set of different polynomial identities applying the most frequently used technique known as Streb’s classification. Finally, in the last section, these results of the foregoing sections are further extended to a special class of rings called as one sided s - unital rings.
Associative Ring, Factor Subring, Polynomial Constraints, Nilpotent Elements, Commutators, Center of Ring, s - Unital Ring and Commutativity
To cite this article
Mohammad Shadab Khan, On Commutativity of Rings Under Certain Polynomial Constraints, International Journal of Data Science and Analysis. Vol. 4, No. 1, 2018, pp. 13-19. doi: 10.11648/j.ijdsa.20180401.13
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