Title:  HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGS 

Authors:  Bordbar, Hashem (Author) Cristea, Irina (Author) Novak, Michal (Author) 

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Language:  English 

Work type:  Not categorized (r6) 

Tipology:  1.01  Original Scientific Article 

Organization:  UNG  University of Nova Gorica 

Abstract:  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. 

Keywords:  Krasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal 

Year of publishing:  2017 

Number of pages:  3142 

Numbering:  79, 2 

COBISS_ID:  4790011 

URN:  URN:SI:UNG:REP:M8RDASFO 

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