A central quaternionic Nullstellensatz

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Let I be a proper left ideal in the ring H[x1,…,xn] of polynomials in n central variables over the quaternion algebra H. Then there exists a point a=(a1,…,an)∈Hn with aiaj=ajai for all i,j, such that every polynomial in I vanishes at a. This generalizes a theorem of Jacobson, who proved the case n=1. Moreover, a polynomial f∈H[x1,…,xn] vanishes at all common zeroes of polynomials in I if and only if f belongs to the intersection of all completely prime left ideals that contain I – a notion introduced by Reyes in 2010.

Original languageEnglish
Pages (from-to)252-261
Number of pages10
JournalJournal of Algebra
StatePublished - 15 May 2021

Bibliographical note

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© 2021


  • Nullstellensatz
  • Polynomial rings
  • Quaternions


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