doiSerbia

Height of prime hyperideals in Krasner hyperrings

Bordbar Hashem (Faculty of Mathematics, Statistics and Computer Science, Shahid Bahonar University, Kerman, Iran)
Cristea Irina (Center for Systems and Information Technologies, University of Nova Gorica, Slovenia)

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.

Keywords: Hyperring, prime/maximal hyperideal, Noetherian/Artinian hyperring, dimension of a hyperring, height of a primehyperideal