Strong Skew Commutativity Preserving Maps on rings

Abstract

Let A be a unital ring with involution. Assume that A contains a nontrivial symmetric idempotent and φ : A → A is a nonlinear surjective map. We prove that if φ preserves strong skew commutativity, thenRelated results concerning nonlinear strong skew commutativity preserving maps on von Neumann algebras are given.2010 Mathematics subject classification: primary 16N60; secondary 16U80.