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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: 664; Downloads: 19
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Keywords: general hyperring, reducibility, fundamental relation, equivalence
Published in RUNG: 25.08.2021; Views: 1287; Downloads: 43
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Keywords: hypergroup, hyperring, hyperfield, hypermodule, dependence relation, fundamental realtion, fuzzy reducibility
Published in RUNG: 23.06.2020; Views: 2263; Downloads: 0
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Keywords: symmetry, hypergroup, hyperring, hyperfield, fundamental relation, rough set, fuzzy set, multiset, soft set, hyperhomography, BCK-algebra, multiautomatom, artificial neuron, hypergraph
Published in RUNG: 27.03.2020; Views: 2103; Downloads: 0
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Keywords: hypergroup, hyperring, hyperfield, (hyper)homography
Published in RUNG: 25.11.2019; Views: 2375; Downloads: 92
Full text (330,54 KB)