Noncommutativity and noncentral zero divisors

Abstract

Let R be a ring, Z its center, and D the set of zero divisors. For finite noncommutative rings, it is known that D\Z≠∅. We investigate the size of |D\Z| in this case and, also, in the case of infinite noncommutative rings with D\Z≠∅.

Keywords

• Finite noncommutative rings
• infinite noncommutative rings
• central and noncentral zero divisors.