Abstract

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.