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On the Integral Closedness of the RingR[α] ∩ R[1/α]

✍ Scribed by Satoru Taeda; Susumu Oda; Ken-ichi Yoshida

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
105 KB
Volume
216
Category
Article
ISSN
0021-8693

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✦ Synopsis

Throughout this paper, all fields, rings, and algebras are assumed to be commutative with unity. Our special notation is indicated below, and our w x general reference for unexplained technical terms is M1 .

In what follows, we use the following notation unless otherwise specified:

R is a Noetherian integral domain.

X s X q X q иии q , the minimal polynomial of ␣ ␣ 1 d over K. d Ž . I [ F R : , which is an ideal of R. w ␣ x is1 R i I [ R : aR for a g K.

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