Regular Parameter Elements and Regular Local Hyperrings

Hashem Bordbar and Irina Cristea
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Hashem Bordbar: Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia
Irina Cristea: Centre for Information Technologies and Applied Mathematics, University of Nova Gorica, 5000 Nova Gorica, Slovenia

Mathematics, 2021, vol. 9, issue 3, 1-13

Abstract: Inspired by the concept of regular local rings in classical algebra, in this article we initiate the study of the regular parameter elements in a commutative local Noetherian hyperring. These elements provide a deep connection between the dimension of the hyperring and its primary hyperideals. Then, our study focusses on the concept of regular local hyperring R , with maximal hyperideal M , having the property that the dimension of R is equal to the dimension of the vectorial hyperspace M M 2 over the hyperfield R M . Finally, using the regular local hyperrings, we determine the dimension of the hyperrings of fractions.

Keywords: Krasner hyperring; prime/maximal hyperideal; length of hypermodules; regular local hyperring; parameter elements (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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