Zero Divisor Manifolds

TL;DR

This paper introduces the concept of zero divisor manifolds within the framework of $R^{(2)}$-modules, generalizing classical geometric structures and initiating the study of their symplectic counterparts.

Contribution

It develops foundational properties of $R^{(2)}$-modules, defines zero divisor manifolds, and constructs a projective space generalization, expanding the scope of geometric and algebraic structures.

Findings

Defined zero divisor manifolds and explored their properties

Constructed a projective $R^{(2)}$-space generalizing real projective space

Initiated the study of symplectic space analogs for these structures

Abstract

We develop the basic properties of $R^{(2)}$-modules, introduce the concept of zero divisor manifolds, construct projective $R^{(2)}$-space which generalizes the real projective space, and initiate the study of the counterpart of symplectic spaces