Result Details
Height of hyperideals in Noetherian Krasner hyperrings
Cristea Irina, doc. dr., UMAT (FEEC)
Novák Michal, doc. RNDr., Ph.D., UMAT (FEEC)
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.
Krasner hyperring, prime/maximal hyperideal, Noetherian hyperring, height of a prime hyperideal
@article{BUT136500,
author="Hashem {Bordbar} and Irina {Cristea} and Michal {Novák}",
title="Height of hyperideals in Noetherian Krasner hyperrings",
journal="University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics",
year="2017",
volume="79",
number="2",
pages="31--42",
issn="1223-7027",
url="https://www.scientificbulletin.upb.ro/SeriaA_-_Matematica_si_fizica_aplicate.php#"
}