Height of Prime Hyperideals in Krasner Hyperrings

Abstract

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.