2020/01/02 by Henry Chimal-Dzul, Chimal-Dzul, Henry, Steve Szabo +1
Mathematics · #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA
paper · pdf · doi:10.48550/arxiv.2001.00305
arxiv created 2020/01/02 · arxiv updated 2020/01/03
It has recently been shown that a minimal reversible nonsymmetric ring has order 256 answering a questioned original posed in a paper on a taxonomy of 2-primal rings. Answers to similar questions on minimal rings relating to this taxonomy were also answered in a related work. One type of minimal ring that was left out of that report, was a minimal abelian reflexive nonsemicommutative ring. In this work it is shown that a minimal abelian reflexive nonsemicommutative ring is of order 256 an example of which is F2D8. This is a consequence of the other primary result which is that a finite abelian reflexive ring of order pk for some prime p and k < 8 is reversible.