Automorphisms of the endomorphism semigroup of a polynomial algebra

A. Belov-Kanel, R. Lipyanski

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


We describe the automorphism group of the endomorphism semigroup End(K[x1,...,xn]) of ring K[x1,...,xn] of polynomials over an arbitrary field K. A similar result is obtained for automorphism group of the category of finitely generated free commutative-associative algebras of the variety CA commutative algebras. This solves two problems posed by B. Plotkin (2003) [18, Problems 12 and 15].More precisely, we prove that if. AutEnd(K[x1,...,xn]) then there exists a semi-linear automorphism s:K[x1,...,xn]K[x1,...,xn] such that (g)=sgs1 for any gEnd(K[x1,...,xn]). This extends the result obtained by A. Berzins for an infinite field K.

Original languageEnglish
Pages (from-to)40-54
Number of pages15
JournalJournal of Algebra
Issue number1
StatePublished - 1 May 2011


  • Kronecker endomorphism
  • Polynomial algebra
  • Rank endomorphism
  • Semi-inner automorphism
  • Variety of commutative-associative algebras

ASJC Scopus subject areas

  • Algebra and Number Theory


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