Closed Polynomials in Polynomial Rings over Unique Factorization Domains |
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| Authors: | Masaya Kato Hideo Kojima |
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| Affiliation: | 1. Graduate School of Science and Technology , Niigata University , Niigata , Japan kojima@math.sc.niigata-u.ac.jp;3. Department of Mathematics, Faculty of Science , Niigata University , Niigata , Japan |
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| Abstract: | ![]()
Let R be a UFD, and let M(R, n) be the set of all subalgebras of the form R[f], where f ∈ R[x 1,…, x n ]?R. For a polynomial f ∈ R[x 1,…, x n ]?R, we prove that R[f] is a maximal element of M(R, n) if and only if it is integrally closed in R[x 1,…, x n ] and Q(R)[f] ∩ R[x 1,…, x n ] = R[f]. Moreover, we prove that, in the case where the characteristic of R equals zero, R[f] is a maximal element of M(R, n) if and only if there exists an R-derivation on R[x 1,…, x n ] whose kernel equals R[f]. |
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| Keywords: | Closed polynomial Derivation |
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