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Extending the notion of dimension of a hyperring, we introduce the concept of height of a prime hyperideal of a hyperring, similarly as in ring theory, and we present some basic properties and relations with the dimension notion. In the second part of the article we illustrate some results concerning the height of prime hyperideals in Noetherian/Artinian hyperrings. 2010 Mathematics Subject Classification. Primary 20N20 Keywords. Hyperring, prime/maximal hyperideal, Noetherian/Artinian hyperring, dimension of a hyperring, height of a prime hyperideal

In this paper we introduce the notion of composition hyperring. We show that the composition structure of a composition hyperring is determined by a class of its strong multiendomorphisms. Finally, the three isomorphism theorems of ring theory are derived in the context of composition hyperrings.

Abstract:The γ * -relation de ned on a general hyperring R is the smallest strongly regular relation such that the quotient R γ * is a ring. In this note we consider a particular class of hyperrings, where we de ne a new equivalence, called ε * m , smaller than γ * and we prove it is the smallest strongly regular relation on such hyperrings such that the quotient R ε * m is a ring. Moreover, we introduce the concept of m-idempotent hyperrings, show that they are a characterization for Krasner hyper elds, and that ε * m is a new exhibition for γ * on the above mentioned subclass of m-idempotent hyperrings.