JP Journal of Algebra, Number Theory and Applications
Volume 1, Issue 1, Pages 47 - 56
(April 2001)
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FLATNESS
AND FAITHFUL FLATNESS OF A TWO-GENERATOR EXTENSION
R[a,
b]
OF A NOETHERIAN DOMAIN R
Kiyoshi Baba (Japan) and Ken-Ichi Yoshida (Japan)
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Abstract: Let
a
and b
be anti-integral elements over a Noetherian
domain R. Set A = R[a,
b],
Iab
= {a Î
R; ab
Î
R[a]}and
Iab
= {a Î
R; aa
Î
R[b]}.Under
the condition Iab
+ Iba
= R, we study flatness, faithful
flatness, exclusiveness, blowing-up locus and
unramification of the extension A/R. |
Keywords and phrases: anti-integral
element, flatness, faithful flatness, exclusiveness,
blowing-up locus, ramification, étale extension. |
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