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 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
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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
. |
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ISSN: | 1678-7544 1678-7714 |
DOI: | 10.1007/s00574-017-0046-8 |