Some Properties of Multiplicative Hv-Rings of Polynomials over Multiplicative Hyperrings. (27th October 2014)

• Record Type: Journal Article
• Authors: Dasgupta, Utpal
• Other Names: Kelarev Andrei V. Academic Editor.
• Is Part Of: Algebra. Volume 2014(2014)
• Publication Date: 2014-10-27
• Subjects: Algebra -- Periodicals; Algebra; Electronic journals; Periodicals; 512.005
• DOI: 10.1155/2014/392902
• Languages: English
• ISSNs: 2314-4106

Abstract

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 .