Finitely generated rings obtained from hyperrings through the fundamental relations | Zendy

S. Mirvakili | Zendy; P. Ghiasvand | Zendy; Bijan Davvaz | Zendy

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Finitely generated rings obtained from hyperrings through the fundamental relations

Author(s) -

S. Mirvakili,

P. Ghiasvand,

Bijan Davvaz

Publication year - 2020

Publication title -

boletim da sociedade paranaense de matemática

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.347

H-Index - 15

eISSN - 2175-1188

pISSN - 0037-8712

DOI - 10.5269/bspm.40500

Subject(s) - omega , commutative property , combinatorics , ring (chemistry) , finitely generated abelian group , mathematics , commutative ring , physics , discrete mathematics , quantum mechanics , chemistry , organic chemistry

In this article, we introduce and analyze a strongly regular relation ω A on a hyperring R such that in a particular case we have |R/ω A | ≤ 2 or R/ω A =< ω∗ A (a) >, i.e., R/ω∗ A is a finite generated ring. Then, by using the notion of ω∗ A -parts, we investigate the transitivity condition of ωA. Finally, we investigate a strongly regular relation χ∗ A on the hyperring R such that R/χ∗ A is a finitely generated commutative ring.

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