The aim of this paper is to generalize the results in [1] and [13]. Here, we are interested in two problems concerning certain classes of near rings satisfying one of the following polynomials identities : (*) For each x, y in a near-ring N , there exist positive integers t = (x, y) ≥ 1 and s = s (x, y) > 1 such that xy = ±y s x t. (* *) For each x, y in a near-ring N , there exist positive integers t = t (x, y) ≥ 1 and s = s (x, y) > 1 such that xy = ±x t y s .

We study the commutativity of certain class of rings, na me/y rings with unity 1 and right s-unital under each of the following properties [yxm-xn f (y) xP , x] = O, [yxm + xn f (y) xP, x) = O, where f (t) is a polynomial in t 2 Z [t] varying with pair of ring elements x, y and m, n, p are fixed non-negative integers. M oreover, the results ha ve 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.

No abstract

Let R be an associative rlng with unity. It is proved that if R satisfies Ohe polynomial identity Ix n y ymxn, x] 0 (m I, n > I), then R is commutative. Two or more related results are also obtained.

In this paper, we study the creation property of projective and forgetful functors vi a genera/ized pu/lback (GP B) and generalized pushout (GPO) structures and also discus sorne general resu/ts.