On Finite and Infinite NeutroRings of Type-NR[8,9]

Abstract

NeutroRings are alternatives to the classical rings and they are of different types. NeutroRings in some cases exhibit different algebraic properties, and in some cases they exhibit algebraic properties similar to the classical rings. The objective of this paper is to revisit the concept of NeutroRings and study finite and infinite NeutroRings of type-NR[8,9]. In NeutroRings of type-NR[8,9], the left and right distributive axioms are taking to be either partially true or partially false for some elements; while all other classical laws and axioms are taking to be totally true for all the elements. Several examples and properties of NeutroRings of type-NR[8,9] are presented. NeutroSubrings, NeutroIdeals, NeutroQuotientRings and NeutroRingHomomorphisms of the NeutroRings of type-NR[8,9] are studied with several interesting examples and their basic properties are presented. It is shown that in NeutroRings of type-NR[8,9], the fundamental theorem of homomorphisms of the classical rings holds.