Left ideals of polynomial rings in several indeterminates

Louis H. Rowen

Research output: Contribution to journalArticlepeer-review


We consider maximal left ideals L of the polynomial ring FORMUIA OMITTED for R noncommutative. In §1 we reprove and generalize Resco’s result that any maximal left ideal L is generated by < n elements whenever R is simple Artinian, and obtain more precise information about the generators when R satisfies a PI. In many instances, fewer than n generators suffice; this is considered in §3, by means of various examples. In §2 we see by a straightforward argument that L has bounded height as a prime left ideal whenever R is a simple PI-ring but this does not hold in general for R simple Artinian.

Original languageEnglish
Pages (from-to)2263-2279
Number of pages17
JournalCommunications in Algebra
Issue number6
StatePublished - Jan 1995

Bibliographical note

Funding Information:
* Research supported in part by US-Israel Binational Science Foundation grant #92-00255/1


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