Structure of rings satisfying certain polynomial identities

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.

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...

A Note on Rings with Certain Variable Identities

It is proved that certain rings satisfying generalized-commutator constraints of the form [x n n n y y y 0 with m and n depending on x and y, mst have nll commutator ideal. KEY WDRDS AND PHRASES. Commutator ideal, periodic ring. 1980 AMS SUBJECT CLASSIFICATION CODE. 16A70.

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.