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- W2940983148 abstract "Abstract Let k be a field, let {mathfrak{A}_{1}} be the k -algebra {k[x_{1}^{pm 1},dots,x_{s}^{pm 1}]} of Laurent polynomials in {x_{1},dots,x_{s}} , and let {mathfrak{A}_{2}} be the k -algebra {k[x,y]} of polynomials in the commutative indeterminates x and y . Let {sigma_{1}} be the monomial k -automorphism of {mathfrak{A}_{1}} given by {A=(a_{i,j})in GL_{s}(mathbb{Z})} and {sigma_{1}(x_{i})=prod_{j=1}^{s}x_{j}^{a_{i,j}}} , {1leq ileq s} , and let {sigma_{2}in{mathrm{Aut}}_{k}(k[x,y])} . Let {D_{i}} , {1leq ileq 2} , be the ring of fractions of the skew polynomial ring {mathfrak{A}_{i}[X;sigma_{i}]} , and let {D_{i}^{bullet}} be its multiplicative group. Under a mild restriction for {D_{1}} , and in general for {D_{2}} , we show that {D_{i}^{bullet}} , {1leq ileq 2} , contains a free subgroup. If {i=1} and {s=2} , we show that a noncentral normal subgroup N of {D_{1}^{bullet}} contains a free subgroup." @default.
- W2940983148 created "2019-05-03" @default.
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- W2940983148 date "2019-05-01" @default.
- W2940983148 modified "2023-09-24" @default.
- W2940983148 title "Free subgroups in k(x 1,... ,x n )(X;σ) and k(x,y)(k;σ)" @default.
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- W2940983148 doi "https://doi.org/10.1515/forum-2017-0248" @default.
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