| Title: | HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGS |
|---|
| Authors: | ID Bordbar, Hashem, Shahid Bahonar University, Iran (Author)
ID Cristea, Irina Elena, University of Nova Gorica, Slovenia (Author)
ID Novak, Michal, Brno University of Technology, Czech Republic (Author) |
|---|
| Files: |
This document has no files that are freely available to the public. This document may have a physical copy in the library of the organization, check the status via COBISS.  |
|---|
| Language: | English |
|---|
| Work type: | Not categorized |
|---|
| Typology: | 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 |
|---|
| Publication version: | Version of Record |
|---|
| Year of publishing: | 2017 |
|---|
| Number of pages: | 31-42 |
|---|
| Numbering: | 2, 79 |
|---|
| PID: | 20.500.12556/RUNG-3106-eea6aff8-499f-20b3-44f1-8929aa52e57a |
|---|
| COBISS.SI-ID: | 4790011 |
|---|
| NUK URN: | URN:SI:UNG:REP:M8RDASFO |
|---|
| Publication date in RUNG: | 01.06.2017 |
|---|
| Views: | 4511 |
|---|
| Downloads: | 0 |
|---|
| Metadata: |     |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
