A NOTE ON CONSTRUCTION OF MODULO AG-GROUPOIDS OF POLYNOMIALS

Abstract

In general, the concept of polynomials of degree  with coefficients from  (group of integers modulo ), is associative and commutative under the binary operations of usual addition. While, in this manuscript we define such binary operations polynomials of degree  with coefficients from , which are nonassociative and noncommutative, and thus form various AG-groupoids and AG-groups of different properties. The constructions of these structures are provided, and various properties of these structures are investigated.

Keywords : AG-groupoids of polynomials; Transitively commutative AG-groupoid; AG-band; Cancellative AG-groupoid; -AG-groupoid; AG-groups of polynomials