Some Properties of Multiplicative Hv-Rings of Polynomials over Multiplicative Hyperrings

Abstract

The set of all polynomials Rx, over a multiplicative hyperring R, +, ·, form a commutative group with respect to the component-wise addition (+) of the polynomials. For polynomials f, g in Rx, f*g is a set of polynomials whose k+1th components k∈N∪0 are chosen from the set ∑i+j=kai·bj, where ai and bj are the i+1th and the j+1th components of f and g, respectively. A multiplicative hyperring is polynomially structured if the hyperstructure Rx, +, * is a multiplicative Hv-ring. The purpose of the paper is to study the properties of the multiplicative Hv-ring Rx, +, *, corresponding to those of a polynomially structured multiplicative hyperring R.