On \(H_v\)-rings and \(H_v\)-representations (Q1808829)

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.