Unions of chains of primes

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

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)1451-1461
Number of pages11
JournalJournal of Pure and Applied Algebra
Volume220
Issue number4
DOIs
StatePublished - 1 Apr 2016

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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