Automorphisms of Ideals of Polynomial Rings

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2018
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Macedo, Tiago [UNIFESP]
Mello, Thiago Castilho de [UNIFESP]
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Let R be a commutative integral domain with unit, f be a nonconstant monic polynomial in R[t], and be the ideal generated by f. In this paper we study the group of R-algebra automorphisms of the R-algebra without unit . We show that, if f has only one root (possibly with multiplicity), then . 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 is a cyclic group and its order can be completely determined by analyzing the roots of f.
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Bulletin Of The Brazilian Mathematical Society. Heidelberg, v. 49, n. 1, p. 1-15, 2018.
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