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\(H_v\)-ring of fractions

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Τίτλος: \(H_v\)-ring of fractions
Συγγραφείς: Darafsheh, M. R., Davvaz, B.
Στοιχεία εκδότη: Forum Editrice Universitaria Udinese Srl, Udine
Θεματικοί όροι: strong homomorphisms, strong multiplicatively closed subsets, hyperstructures, hyperrings, fundamental structures, Generalizations, commutative hyperrings, Hypergroups, \(H_v\)-rings, \(H_v\)-rings of fractions
Περιγραφή: The paper deals with a special class of algebraic structures, more general than the hyperstructures, called \(H_v\)-structures. The notions of hyperring and \(H_v\)-ring are used. More precisely, the definition of strong multiplicatively closed subset \(S\) of a commutative hyperring \((R,+,\cdot)\), is introduced. Therefore, given a commutative hyperring \(R\) with a scalar unit, the \(H_v\)-ring of fractions \((S^{-1}R,\oplus,\otimes)\) is defined. Some results concerning this \(H_v\)-ring \(S^{-1}R\) using strong homomorphisms and \(H_v\)-ideals are proved. These results are transferred to the corresponding fundamental structures.
Τύπος εγγράφου: Article
Περιγραφή αρχείου: application/xml
Σύνδεσμος πρόσβασης: https://zbmath.org/1418057
Αριθμός Καταχώρησης: edsair.c2b0b933574d..a0c4d43e9e9c3c347f480dcc5d944d49
Βάση Δεδομένων: OpenAIRE
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PubType: Academic Journal
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  Data: Forum Editrice Universitaria Udinese Srl, Udine
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  Data: <searchLink fieldCode="DE" term="%22strong+homomorphisms%22">strong homomorphisms</searchLink><br /><searchLink fieldCode="DE" term="%22strong+multiplicatively+closed+subsets%22">strong multiplicatively closed subsets</searchLink><br /><searchLink fieldCode="DE" term="%22hyperstructures%22">hyperstructures</searchLink><br /><searchLink fieldCode="DE" term="%22hyperrings%22">hyperrings</searchLink><br /><searchLink fieldCode="DE" term="%22fundamental+structures%22">fundamental structures</searchLink><br /><searchLink fieldCode="DE" term="%22Generalizations%22">Generalizations</searchLink><br /><searchLink fieldCode="DE" term="%22commutative+hyperrings%22">commutative hyperrings</searchLink><br /><searchLink fieldCode="DE" term="%22Hypergroups%22">Hypergroups</searchLink><br /><searchLink fieldCode="DE" term="%22%5C%28H%5Fv%5C%29-rings%22">\(H_v\)-rings</searchLink><br /><searchLink fieldCode="DE" term="%22%5C%28H%5Fv%5C%29-rings+of+fractions%22">\(H_v\)-rings of fractions</searchLink>
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  Data: The paper deals with a special class of algebraic structures, more general than the hyperstructures, called \(H_v\)-structures. The notions of hyperring and \(H_v\)-ring are used. More precisely, the definition of strong multiplicatively closed subset \(S\) of a commutative hyperring \((R,+,\cdot)\), is introduced. Therefore, given a commutative hyperring \(R\) with a scalar unit, the \(H_v\)-ring of fractions \((S^{-1}R,\oplus,\otimes)\) is defined. Some results concerning this \(H_v\)-ring \(S^{-1}R\) using strong homomorphisms and \(H_v\)-ideals are proved. These results are transferred to the corresponding fundamental structures.
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      – SubjectFull: strong homomorphisms
        Type: general
      – SubjectFull: strong multiplicatively closed subsets
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      – SubjectFull: hyperstructures
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      – SubjectFull: \(H_v\)-rings
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      – SubjectFull: \(H_v\)-rings of fractions
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