Core Partial Order in Rings with Involution

Abstract

Let $R$ be a unital ring with involution. We give several characterizations and properties of core partial order in $R$.
In particular, we investigate the reverse order law $(ab)^{\tiny\textcircled{\tiny\#}}=b^{\tiny\textcircled{\tiny\#}}a^{\tiny\textcircled{\tiny\#}}$
for two core invertible elements $a,b\in R$.
Some relationships between core partial order and other partial orders are obtained.