Some Properties of Multiplicative Hv-Rings of Polynomials over Multiplicative Hyperrings. (27th October 2014) - Dasgupta, Utpal
Abstract : The set of all polynomials R x, over a multiplicative hyperring R,   +,   ·, form a commutative group with respect to the component-wise addition (+) of the polynomials. For polynomials f, g in R x, f * g is a set of polynomials whose k + 1 th components k ∈ N ∪ 0 are chosen from the set ∑ i + j = k a i · b j, where a i and b j are the i + 1 th and the j + 1 th components of f and g, respectively. A multiplicative hyperring is polynomially structured if the hyperstructure R x,   +,   * is a multiplicative H v -ring. The purpose of the paper is to study the properties of the multiplicative H v -ring R x,   +,   *, corresponding to those of a polynomially structured multiplicative hyperring R .