• HOMOMORPHISM NEAR-FIELD SPACE OVER A NEAR-FIELD

Abstract

In depth study of near-rings, near-fields, various types of d - near-rings is motivated to extend the feature of near-field spaces over near-rings as well as near-fields and by consideration of the system generated by the endomorphisms of  a ( not necessarily commutative) near-field space. Such endomorphism near-field spaces also furnish the motivation for the concept of a distributively generated (d.g.) near-field space. Although Dr N V Nagendram as author, d.g. near-field spaces have been extensively studied, little is known about the structure of endomorphism near-field spaces. In this paper results are presented which enable one to give the elements of the endomorphism near-field space of a near-field space over a near-field. Also some results relating to the right sub near-field space structure of an endomorphism near-field space are presented. These concepts are applied to present a detailed picture of the properties of the endomorphism near-field space of (S_n, +).