Free subsemigroups in automorphism group of a polynomial ring of two variables over number fields

Zh. I. Dovghey, M. I. Sumaryuk


Sufficient conditions under which the semigroup generated by two automorphism of the polynomial ring in two variables over a number field $P$ will be free are given. The set of free finitely generated subsemigroups of the triangle automorphism subgroup in $AutP[x; y]$ and the set of non-free finitely generated of semigroups of this groups are compared in categorial sense of Baire.

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