• PART - I ON NON-ASSOCIATIVE G-SEMI SUB NEAR-FIELD SPACES OF A G-NEAR-FIELD SPACE OVER NEAR-FIELD (NA-G-SSNFS-G-NFS-NF)

Abstract

In this manuscript we solely devoted to the study and introduction of non-associative G-semi sub near-field space of a G-near-field space over near-field. The study of non-associative G-semi sub near-field space of a G-near-field space over near-field which also called the loop near-field space which is a non-associative structure with respect to the operation ‘+’ which is very unusual in rings. Here in section one we just define non-associative G-semi sub near-field space of a G-near-field space over near-field and define several of its properties. In section two we construct several new types of non-associative G-semi sub near-field space of a G-near-field space over near-field and semi G-semi sub near-field space of a G-near-field space over near-field using mixed direct product.