Let $A$ be a set and $R$ be a relation on $A$ Suppose that $B$ is a subset of $A$ An element $a\in B$ is said to be $R$ minimal in $B$ if and only if there is no $x\in B$ such that $xRa$ An $R$ minimal element in $A$ is simply called $R$ minimal.

From this definition, it is evident that if $A$ has an $R$ minimal element, then $R$ is not reflexive. However, the definition of $R$ minimality is sometimes adjusted slightly so as to allow reflexivity: $a\in B$ is $R$ minimal (in $B$ iff the only $x\in B$ such that $xRa$ is when $x=a$

Remark. Using the second definition, it is easy to see that when $R$ is a partial order, then an element $a$ is $R$ minimal iff it is minimal.