Automorphisms of Ideals of Polynomial Rings

Let R be a commutative integral domain with unit, f be a nonconstant monic polynomial in R [ t ], and I f ⊂ R [ t ] be the ideal generated by f . In this paper we study the group of R -algebra automorphisms of the R -algebra without unit I f . We show that, if f has only one root (possibly with mult...

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Veröffentlicht in:Boletim da Sociedade Brasileira de Matemática 2018-03, Vol.49 (1), p.1-15
Hauptverfasser: Macedo, Tiago, de Mello, Thiago Castilho
Format: Artikel
Sprache:eng
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Zusammenfassung:Let R be a commutative integral domain with unit, f be a nonconstant monic polynomial in R [ t ], and I f ⊂ R [ t ] be the ideal generated by f . In this paper we study the group of R -algebra automorphisms of the R -algebra without unit I f . We show that, if f has only one root (possibly with multiplicity), then Aut ( I f ) ≅ R × . We also show that, under certain mild hypothesis, if f has at least two different roots in the algebraic closure of the quotient field of R , then Aut ( I f ) is a cyclic group and its order can be completely determined by analyzing the roots of f .
ISSN:1678-7544
1678-7714
DOI:10.1007/s00574-017-0046-8