Journal Name:
- İstanbul Üniversitesi Fen Fakültesi Matematik, Fizik ve Astronomi Dergisi
| Author Name | University of Author | Faculty of Author |
|---|---|---|
Abstract (2. Language):
In the present paper, we prove the commutativity of a ring with unity satisfying any one of the following properties:
{1 - p(yxm)} [yxm - xrb(yxm) xs,x]{l - q(yxm)} = 0,
ys[x,yn] = g(x)[x2f{x),y]h(x) and [x,yn] yt = g(x)[x2f(x), y]h(x),
for some b(X) G X2Z[X], and p{X),q(X) G XZ[X] and f(X)J(X),g(X) g(X),h(X),h(X) G Z[X], where m > 0, r > 0, s > 0, n > 0, t > 0 are integers. Further, we extend these results to the case when integral exponents in the underlying conditions are no longer fixed, rather they depend on the pair of ring elements x, y for their values. Moreover, it is also shown that the above result is true for s-unital rings. Finally, our results generalize many known commutativity theorems.
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FULL TEXT (PDF):
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