Dedekind’s Criterion and Integral Bases
Keyword(s):
Abstract Let R be a principal ideal domain with quotient field K, and L = K(α), where α is a root of a monic irreducible polynomial F (x) ∈ R[x]. Let ℤL be the integral closure of R in L. In this paper, for every prime p of R, we give a new efficient version of Dedekind’s criterion in R, i.e., necessary and sufficient conditions on F (x) to have p not dividing the index [ℤL: R[α]], for every prime p of R. Some computational examples are given for R = ℤ.
1980 ◽
Vol 32
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pp. 1361-1371
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2019 ◽
Vol 18
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pp. 1950104
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2016 ◽
Vol 95
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pp. 14-21
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2018 ◽
Vol 148
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pp. 731-750
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2012 ◽
Vol 11
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pp. 1250063
1963 ◽
Vol 15
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pp. 755-765
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1986 ◽
Vol 23
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pp. 851-858
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