Abstract

The purpose of the article is to study about homomorphism and anti-homomorphism of spherical cubic bi-ideals of Gamma near-rings $\mathcal{R}_{1}$ and $\mathcal{R}_{2}$. If $\phi: R_{1}\longrightarrow R_{2}$ be a gamma homomorphism and $(\mathscr{CU}_{s_{1}}, R_{1})$, $(\mathscr{CU}_{s_{2}}, R_{2})$ are spherical cubic bi-ideals of gamma near-rings $R_{1}$ and $R_{2}$.Then the image $(\phi(\mathscr{CU}_{s_{1}}),R_{2})$ and pre-image $(\phi^{-1}(\mathscr{CU}_{s_{2}}),R_{1})$ are also spherical cubic bi-ideals of gamma near-rings $R_{2}$ and $R_{1}$. If $\phi: \mathcal{R}_{1}\longrightarrow \mathcal{R}_{2}$ be an epimorphism of gamma near-rings $\mathcal{R}_{1}$ and $\mathcal{R}_{2}$ and $(\mathscr{CU}_{s_{2}}, \mathcal{R}_{2})$ is a SCS of $\mathcal{R}_{2}$ such that $(\phi^{-1}(\mathscr{CU}_{s_{2}}),\mathcal{R}_{1})$ is a SCBI of $\mathcal{R}_{1}$, then $(\mathscr{CU}_{s_{2}}, \mathcal{R}_{2})$ is a SCBI of $\mathcal{R}_{2}$.

Keywords and Phrases

Spherical set, cubic set, $\Gamma$-near-ring, bi-ideal, homomorphism, anti-homomorphism.

A.M.S. subject classification

Primary 16Y30, 03E72; Secondary 16D25.

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