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Regular local hyperrings and hyperdomains
Hashem Bordbar, Irina Elena Cristea, Sanja Rasovic, 2022, original scientific article

Abstract: This paper falls in the area of hypercompositional algebra. In particular, it focuses on the class of Krasner hyperrings and it studies the regular local hyperrings. These are Krasner hyperrings R with a unique maximal hyperideal M having the dimension equal to the dimension of the vectorial hyperspace M. The aim of the paper is to show that any regular local hyperring is a hyperdomain. M2 For proving this, we make use of the relationship existing between the dimension of the vectorial hyperspaces related to the hyperring R and to the quotient hyperring R = R , where a is an element in M \ M2, and of the regularity of R.
Keywords: hyperring, hypermodule, vectorialhyperspace, dimension, regularhyperring, regular parameter element, hyperdomain
Published in RUNG: 27.09.2022; Views: 1167; Downloads: 21
.pdf Full text (258,07 KB)

Height of Prime Hyperideals in Krasner Hyperrings
Irina Elena Cristea, Hashem Bordbar, 2017, original scientific article

Keywords: hyperring, prime/maximal hyperideal, dimension of a hyperring, height of a prime hyperideal
Published in RUNG: 03.01.2018; Views: 3717; Downloads: 0
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