A remark on the classifications of rhotrices as abstract structures

This paper presents additional classifications of rhotrices as abstract structures of Ring, Field, Integral Domain, Principal Ideal Domain and Unique Factorization Domain, as a sort of an additional work to our earlier classifications of rhotrices as algebraic structures of Groups, Semi groups, Monoids and Boolean Algebra. Rhotrix is a new paradigm of matrix theory, concerned with representing arrays of real numbers in mathematical rhomboid form, as an extension of ideas on matrix-tertions and matrix noitrets proposed by Atanassov and Shannon.   Key words: Rhotrices, ring, field, integral domain, principal ideal domain, unique factorization domain.