# Automorphisms of the semigroup End(K[x 1 , . . . , x n ]) Academic Article

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### abstract

• We describe the group G = AutEnd(K[x 1, . . . , x n ]), where K is an arbitrary field. A similar result is obtained also for the automorphism group of the category $\mathcal{C}{\mathcal{A}^{\circ }}$ of finitely generated free commutative-associative algebras of the variety commutative algebras. This solves two problems posed by B. Plotkin ( [4, Problems 12 and 15]).

### publication date

• November 1, 2012