Preserving Zeros of xy and xy*

Abstract

We describe surjective additive maps θ: A → B which preserve zero products, where A is a ring with a nontrivial idempotent and B is a prime ring. We also characterize surjective additive maps θ: A → B such that for all x, y ∈ A we have θ(x)θ(y)* = 0 if and only if xy* = 0. Here A is a unital prime ring with involution that contains a nontrivial idempotent and B is a prime ring with involution.

Key Words:

• Involution
• Martindale rings of quotients
• Maximal rings of quotients
• Prime ring
• Zero product preservers

2000 Mathematics Subject Classification:

• 16N60
• 16W10

Notes

Communicated by I. Swanson.