Commutativity of rings through a Streb's result

Some commutativity results for certain rings

“…where F is a finite with a non-trivial automorphism σ . In 1989, Streb [12] gave a nice classification for non-commutative rings which yields a powerful tool in obtaining a number of commutativity theorems ( [5], [6], and [7]). It follows from the-proof of [6, Corollary 1] that if R is a non-commutative ring with unity 1, then there exists a factorsubring of R which is of type (i), (ii), (iii), (iv) or (v).…”

Commutativity of rings with polynomial constraints

“…In attempts to generalize this result, several authors have considered various special cases of (P) and (P 1 ) (cf. [1], [2], [5], [6], [7], [11], [12], [14], [16]). In most of the cases the underlying polynomials are assumed to be monomials.…”

“…In an attempt to prove commutativity of rings satisfying such conditions, the author [11] has shown that a ring with unity 1 is commutative if, for all x ∈ R, there exist polynomials…”