On \(H_v\)-rings and \(H_v\)-representations
type: Item
instance of: scholarly article
title: On \(H_v\)-rings and \(H_v\)-representations
zbMATH Open document ID: 0938.20058
DOI: 10.1016/S0012-365X(99)00101-6
published in: Discrete Mathematics
publication date: 2000-06-20T00:00:00Z
review text: This paper deals with a very large class of algebraic hyperstructures called by the author \(H_v\)-groups and \(H_v\)-rings. \((H,+)\) is an \(H_v\)-group if: (i) \([(x+ y)+z]\cap[x+(y+z)]\neq\emptyset\); (ii) \(x+H=H=H+x\), for all \(x,y,z\) in \(H\). Also \((R,+)\) is an \(H_v\)-ring if \((R,+)\) is an \(H_v\)-group and (iii) \(x(y+z)\cap(xy+xz)\neq\emptyset\); (iv) \((x+y)z\cap(xz+yz)\neq\emptyset\) for all \(x,y,z\) in \(R\). Some new classes of \(H_v\)-rings are introduced.
Mathematics Subject Classification ID: 20N20
Mathematics Subject Classification ID: 16Y99
zbMATH DE Number: 1369813
zbMATH Keywords: hyperstructures
zbMATH Keywords: \(H_v\)-groups
zbMATH Keywords: \(H_v\)-rings
author: Thomas Vougiouklis
reviewed by: Marin Guţan
MaRDI profile type: Publication
full work available at URL: s0012-365x(99)00101-6
OpenAlex ID: W2577789625
description: scientific article; zbMATH DE number 1369813