SOME COMMUTATIVITY THEOREMS FOR ASSOCIATIVE RINGS WITH CONSTRAINTS INVOLVING A NIL SUDSET

Authors

  • MOHD ASHRAF Department of Mathemat.ics, Karnatak University, Dharwad-580 003; Department of Mathematics, J. M. Institute of Technology, Chitradurga-577 502, India.

DOI:

https://doi.org/10.5556/j.tkjm.22.1991.4613

Keywords:

central elements, nil subset, commutativity, idempotent, left s-unital ring

Abstract

We first prove that a ring $R$ with unity 1 is corrunutalive if and only if for each $x$ in $R$ either $x$ is central or there exists a polynomial $f(t) \in Z[t]$ such that $x- x^2f(x) \in A$, where $A$ is a nil subset of $R$ (not necessarily a subring of $R$) and $R$ stisfies any one of the conditions $[x, x^my- x^py^nx^q] =0$ and $[x,yx^m-x^Py^nx^q]=0$ for all $x,y$ in $R$, where $m\ge 0$, $n >1$, $p \ge 0$, $q \ge 0$ are integers depending on pair of elements $x$, $y$. Further the same result has been extended for one sided $s$-unital rings. Finally a related result for a nil commutative subset $A$ is also obtained.

References

I. S. Jack, "Functions starlike and convex of order alpha", J. London Math. Soc., 2 (3), 469-479, 1971.

P. Rotaru, "Subclasses of starlike functions", Mathematica, 29 (52), 2, 183-191, 1987.

Vinod kumar and S. L. Shukla, "Jakubowski starlike integral operators", J. Austral Math. Soc. (Series A), 37, 117-127, 1984.

Downloads

Published

1991-09-01

How to Cite

ASHRAF, M. (1991). SOME COMMUTATIVITY THEOREMS FOR ASSOCIATIVE RINGS WITH CONSTRAINTS INVOLVING A NIL SUDSET. Tamkang Journal of Mathematics, 22(3), 285–297. https://doi.org/10.5556/j.tkjm.22.1991.4613

Issue

Section

Papers