LAUSR

Polynomial functions in the residue class rings of Dedekind domains

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1 Published in 2019 at "International Journal of Number Theory"

DOI: 10.1142/s1793042119500854

Abstract: In this paper, as an extension of the integer case, we define polynomial functions over the residue class rings of Dedekind domains, and then we give canonical representations and counting formulas for such polynomial functions.… read more here.

Keywords: residue class; rings dedekind; polynomial functions; functions residue ... See more keywords

Chevalley groups of polynomial rings over Dedekind domains

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0 Published in 2019 at "Journal of Group Theory"

DOI: 10.1515/jgth-2019-0100

Abstract: Abstract Let R be a Dedekind domain and G a split reductive group, i.e. a Chevalley–Demazure group scheme, of rank ≥2{\geq 2}. We prove that G⁢(R⁢[x1,…,xn])=G⁢(R)⁢E⁢(R⁢[x1,…,xn]) for any⁢n≥1.G(R[x_{1},\ldots,x_{n}])=G(R)E(R[x_{1},\ldots,x_{n}])\quad\text{for any}\ n% \geq 1. In particular, this extends… read more here.

Keywords: groups polynomial; polynomial rings; group; chevalley groups ... See more keywords