STRUCTURE OF NEAR-RINGS SATISFYING CERTAIN POLYNOMIAL IDENTITIES

On Structure of Certain Periodic Rings and Near-rings

The aim of this work is to study a decomposition theorem for rings satisfying either of the properties xy = xpf(xyx)xq or xy = xpf(yxy)xq , where p = p(x,y), q = q(x,y) are nonnegative integers and f(t)∈ tZ[t] vary with the pair of elements x,y, and further investigate the commutativity of such rings. Other related results are obtained for near-rings.

On Derandomizing Tests for Certain Polynomial Identities

We extract a paradigm for derandomizing tests for polynomial identities from the recent AKS primality testing algorithm. We then discuss its possible application to other tests.

Homomorphic Images of Polynomial Near-rings

A polynomial near-ring can mean one of several things. Here a polynomial near-ring is a near-ring of polynomials with the coefficients from a near-ring in the sense of van der Walt and Bagley. We describe quotients of such polynomial near-rings by principal ideals leading to generalizations of some well-known ring constructions. MSC 2000: 16Y30

Differential Polynomial Rings of Triangular Matrix Rings

Some Polynomial Identities that Imply Commutativity of Rings

In this paper, we establish some commutativity theorems for certain rings with polynomial constraints as follows: Let R be an associative ring, and for all x, y ∈ R, and fixed non-negative integers m > 1, n ≥ 0, r > 0, s ≥ 0, t ≥ 0, p ≥ 0, q ≥ 0 such that P (x, y) = ±Q(x, y), where P (x, y) = ys[x, y]yt and Q(x, y) = xp[xm, yn]ryq. First,it is shown that a semiprime ring R is commutative if and...