An introduction to the theory of algebraic multi-hyperring spaces

Abstract

A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2 which can be used both for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics. In this paper, applying the Smarandaches notion and combining this with hyperrings in hyperring theory, we introduce the notion of multi-hyperring space and initiate a study of multi-hyperring theory. Some characterizations and properties of multihyperring spaces are investigated and obtained. Some open problems are suggested for further study and investigation.

Extended centroid of hyperrings

“…The basic results of hyperstructures and hyperrings are found in [4] and [5]. Also, we refer the reader to see [6,7,8,12,13,14,15,16,17,18]. A well-known type of a hyperring is called the Krasner hyperring.…”

Height of prime hyperideals in Krasner hyperrings

“…This is, till now, the most well known and studied type of hyperrings, called Krasner hyperring. If the addition is a binary operation and the multiplication a binary hypercomposition, then we talk about the multiplicative hyperrings defined by Rota [17], that lately attracted the attention of several researchers (for example, see the papers published in 2014 [2,5,8]). Moreover, in 1973 Mittas [14] introduced the superrings, where both, the addition and the multiplication, are hyperoperations, with the additive hyperstructure being a canonical hypergroup.…”