HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGS
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.
2017
2017-06-01 01:56:08
1033
Krasner hyperring,prime/maximalhyperideal,Noetherian hyperring,height of a prime hyperideal
r6
Hashem
Bordbar
70
Irina
Cristea
70
Michal
Novak
70
COBISS_ID
3
4790011
URN
14
URN:SI:UNG:REP:M8RDASFO
rezbb0_929561.pdf
141631
Predstavitvena datoteka
2017-06-01 01:56:20
0
Izvorni URL
2017-06-01 01:56:09