Minimal reflexive nonsemicommutative rings

Abstract

It has recently been shown that a minimal reversible nonsymmetric ring has order 256 answering a question originally posed in a paper on a taxonomy of 2-primal rings. In a different work, questions on minimal rings having to do with this taxonomy were also answered. In this work it is shown that a minimal abelian reflexive nonsemicommutative ring also has order 256, a related question left open in these previous works. It is also shown here that [Formula: see text] is such a minimal ring. This is a consequence of the main result of the paper which is that a finite abelian reflexive ring of order [Formula: see text] for some prime [Formula: see text] and [Formula: see text] is reversible.