Unions of chains of primes

Be'eri Greenfeld; Louis H. Rowen; Uzi Vishne

doi:10.1016/j.jpaa.2015.09.011

Unions of chains of primes

Be'eri Greenfeld
, Louis H. Rowen
, Uzi Vishne

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The union of an ascending chain of prime ideals is not always prime. The union of an ascending chain of semi-prime ideals is not always semi-prime. We show that neither one of these properties imply the other. We also show that the number of non-prime unions of subchains in a chain of primes in a PI-algebra does not exceed the PI-class minus one, and this bound is tight.

Original language	English
Pages (from-to)	1451-1461
Number of pages	11
Journal	Journal of Pure and Applied Algebra
Volume	220
Issue number	4
DOIs	https://doi.org/10.1016/j.jpaa.2015.09.011
State	Published - 1 Apr 2016

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V.

Funding

This research was partially supported by a BSF grant no. 206940 .

Funders	Funder number
United States-Israel Binational Science Foundation	206940

Access to Document

10.1016/j.jpaa.2015.09.011

Cite this

@article{9049e15848684e18801eba17165fc49a,

title = "Unions of chains of primes",

abstract = "The union of an ascending chain of prime ideals is not always prime. The union of an ascending chain of semi-prime ideals is not always semi-prime. We show that neither one of these properties imply the other. We also show that the number of non-prime unions of subchains in a chain of primes in a PI-algebra does not exceed the PI-class minus one, and this bound is tight.",

author = "Be'eri Greenfeld and Rowen, \{Louis H.\} and Uzi Vishne",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier B.V.",

year = "2016",

month = apr,

day = "1",

doi = "10.1016/j.jpaa.2015.09.011",

language = "אנגלית",

volume = "220",

pages = "1451--1461",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier B.V.",

number = "4",

}

TY - JOUR

T1 - Unions of chains of primes

AU - Greenfeld, Be'eri

AU - Rowen, Louis H.

AU - Vishne, Uzi

PY - 2016/4/1

Y1 - 2016/4/1

N2 - The union of an ascending chain of prime ideals is not always prime. The union of an ascending chain of semi-prime ideals is not always semi-prime. We show that neither one of these properties imply the other. We also show that the number of non-prime unions of subchains in a chain of primes in a PI-algebra does not exceed the PI-class minus one, and this bound is tight.

AB - The union of an ascending chain of prime ideals is not always prime. The union of an ascending chain of semi-prime ideals is not always semi-prime. We show that neither one of these properties imply the other. We also show that the number of non-prime unions of subchains in a chain of primes in a PI-algebra does not exceed the PI-class minus one, and this bound is tight.

UR - https://www.scopus.com/pages/publications/84960228826

U2 - 10.1016/j.jpaa.2015.09.011

DO - 10.1016/j.jpaa.2015.09.011

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:84960228826

SN - 0022-4049

VL - 220

SP - 1451

EP - 1461

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 4

ER -

Unions of chains of primes

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this