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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.
Found in: ključnih besedah
Summary of found: ...the notion of height of a prime hyperideal in a Krasner hyperring. In this note...
Keywords: Krasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal
Published: 01.06.2017; Views: 3658; Downloads: 0
Fulltext (138,31 KB)

Found in: ključnih besedah
Summary of found: ...hyperring, prime/maximal hyperideal, dimension of a hyperring, height of a...
Keywords: hyperring, prime/maximal hyperideal, dimension of a hyperring, height of a prime hyperideal
Published: 03.01.2018; Views: 2851; Downloads: 0
Fulltext (257,02 KB)

Found in: ključnih besedah
Summary of found: ...Krasner hyperring, prime/maximal hyperideal, length of hypermodules, regular local hyperring,...
Keywords: Krasner hyperring, prime/maximal hyperideal, length of hypermodules, regular local hyperring, parameter elements
Published: 27.01.2021; Views: 1581; Downloads: 65
Fulltext (0,00 KB)
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