On Commutativity of Assosymmetric Rings With Some Identities

Abstract

In this paper we present some results on assosymmetric rings satisfying some identities. A non-associative ring is defined as a nilpotent if there exists $k \geq0$ such that any product having k elements is zero. A ring is solvable if the chain of sub rings $S \supseteq S^{2} \supseteq (S^{2})^{2} \supseteq \dots$ reaches zero in a finite number of steps. While solvable associative rings are obviously nilpotent, solvable alternative rings need not be nilpotent [1].