“Anti – Homomorphism in Rings”

Author Name : Dr. Dale T. B.

ABSTRACT

In this chapter, the concept of anti - homomorphisms in  Rings in studied and many results are established.

Keyword: Ring, Anti-homomorphism,anti-monorphism, anti-isomorphism

INTRODUCTION

The concept of anti – homomorphism in groups and rings is not found much in the literature. Authors like Jocobson Neal McCoy and Zariski and Samul have touched this concept in a lighter way.  The reason is perhaps that the composition of two anti-homomorphisms is not an anti-homomorphism, but a homomorphism. This discouraged the mathematicians to move further. In 2006, G. Gopalakrishnamoorthy defined a new composition of two anti-homomorphisms so that the composition of two anti-homomorphisms with respect to the new composition is again an anti-homomorphism.In this paper we study the concept  of  anti - homomorphisms  in Rings.