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21.
Overview on the height of a hyperideal in Krasner hyperrings
Hashem Bordbar, Irina Elena Cristea, Michal Novak, 2017, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: Krasner hyperring, prime hyperideal, Noetherian hyperring
Objavljeno v RUNG: 30.08.2017; Ogledov: 4044; Prenosov: 0
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22.
A note on composition (m,n)-hyperrings
Morteza Norouzi, Irina Elena Cristea, 2017, izvirni znanstveni članek

Opis: Based on the concepts of composition ring and composition hyperring, in this note we introduce the notion of composition structure for (m,n)-hyperrings and study the connections with composition hyperrings. Moreover we show that particular strong endomorphisms of (m,n)-hyperrings can determine the composition structure of such (m,n)-hyperrings. Finally, the three isomorphism theorems are presented in the case of composition (m, n)-hyperrings, showing that they are not a pure extension of those for composition hyperrings.
Ključne besede: n-hypergroup, (m, n)-hyperring, composition hyperideal
Objavljeno v RUNG: 13.07.2017; Ogledov: 4254; Prenosov: 0
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23.
Hyperrings with n -ary composition hyperoperation
Morteza Norouzi, Irina Elena Cristea, 2017, izvirni znanstveni članek

Opis: Based on the concepts of composition ring and composition hyperring, in this note we introduce the notion of $n$-ary composition hyperring and study the connections with composition hyperrings. Moreover we show that special strong multiendomorphisms of hyperrings can determine the $n$-ary composition structure of a such hyperring and also a subclass of $n$-ary composition hyperrings. Finally, the three isomorphism theorems are studied in the framework of $n$-ary composition hyperrings.
Ključne besede: n-ary hypergroup, (m, n)-hyperring, composition hyperring, n-ary composition hyperideal
Objavljeno v RUNG: 10.07.2017; Ogledov: 4245; Prenosov: 0
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24.
HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGS
Hashem Bordbar, Irina Elena Cristea, Michal Novak, 2017, izvirni znanstveni članek

Opis: Inspired by the classical concept of height of a prime ideal in a ring, we proposed in a precedent paper the notion of height of a prime hyperideal in a Krasner hyperring. In this note we first generalize some results concerning the height of a prime hyperideal in a Noetherian Krasner hyperring, with the intent to extend this definition to the case of a general hyperideal in a such hyperring. The main results in this note show that, in a commutative Noetherian Krasner hyperring, the height of a minimal prime hyperideal over a proper hyperideal generated by n elements is less than or equal to n, the converse of this claim being also true. Based on this result, it can be proved that the height of such a prime hyperideal is limited by the height of a corresponding quotient hyperideal.
Ključne besede: Krasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal
Objavljeno v RUNG: 01.06.2017; Ogledov: 4878; Prenosov: 0
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