THE NON-COMMUTATIVE FULL RHOTRIX RING AND ITS SUBRINGS

Abstract

This paper presents the triple consisting of the set of all rhotrices of size n with entries in an arbitrary ring F; and together with the operations of rhotrix addition ‘+’ and row-column based method for rhotrix multiplication;  , so as to introduce it as “the concept of non-commutative full rhotrix ring”, and study its properties. A number of subrings of are uncovered. Next, the paper shows that a particular subring of the non-commutative full rhotrix ring is embedded in a particular subring of the well-known non-commutative full matrix ring . Furthermore, isomorphic relationships between some subrings of are investigated.