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In this paper, we study affine commutative algebraic monoid structures onaffine spaces over an arbitrary field of characteristic zero. We obtain fullclassification of such structures on $\mathbb{A}_K^2$ and $\mathbb{A}_K^3$ anddescribe some generalizations on $\mathbb{A}_K^n$ for any dimension $n$.

Twisted forms of commutative monoid structures on affine spaces