Generalized Centroid of Hyperrings Yazarli, Hasret; Davvaz, Bijan; Yilmaz, Damla
Discussiones mathematicae. General algebra and applications,
03/2022, Volume:
42, Issue:
1
Journal Article
Peer reviewed
Open access
In this paper, the notion of generalized centroid is applied to hyperrings. We show that the generalized centroid
of a semiprime hyperring
is a regular hyperring. Also, we show that if
is a ...hyperfield, then
is a prime hyperring.
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 $ \frac{M}{M^2} $. The aim of the paper is to show that any regular local hyperring is a hyperdomain. 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 $ \overline{R} = \frac{R}{\langle a\rangle} $, where $ a $ is an element in $ M\setminus M^2 $, and of the regularity of $ \overline{R} $.
