Introduction to AntiRings

Abstract

The objective of this paper is to introduce the concept of AntiRings. Several examples of AntiRings are
presented. Specifically, certain types of AntiRings and their substructures are studied. It is shown that nonempty subsets
of an AntiRing can be AntiRings with algebraic properties different from the algebraic properties of the parent AntiRing
under the same binary operations. AntiIdeals, AntiQuotientRings and AntiRingHomomorphisms are studied with several
examples. It is shown that the quotient of an AntiRing factored by an AntiIdeal can exhibit algebraic properties different
from the algebraic properties of the AntiRing.