Bicomplex Modules with Indefinite Inner Product

In this article we provide a systematic investigation of bicomplex indefinite inner product modules. Based on the partial ordering defined on the set of hyperbolic numbers, we classify the elements of the modules into positive, negative and neutral types. Our study includes the orthogonality, isotropic elements, maximal non-degenerate submodule, maximal semi definite submodule and ortho-complemented submodules of bicomplex inner product modules. We then decompose such a module fundamentally into a positive definite, a negative definite and a neutral submodules that ensures the existence of a fundamental symmetry associated with a positive definite inner product for non-degenerate case.