JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 1, Pages 145 - 155
(April 2003)
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THE
EXTENSION R[b,
b–1]OF A LINEAR FRACTIONAL TRANSFORM OF AN
ANTI-INTEGRAL ELEMENT
Kiyoshi Baba (Japan) and Ken-Ichi Yoshida (Japan)
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Abstract: Let a
be a non-zero anti-integral element over an
integral domain R and b
be a linear fractional transform of a
, that is,
where
is the group of units of R. We give
a condition for
to coincide with
in terms of a, b, c, d
and generalized denominator ideals
(cf. Theorem 8). Moreover, we give a condition
of where
and
are linear fractional transforms of a
(cf. Theorem 9). We also give a condition of
(cf. Theorem 11). |
Keywords and phrases: generalized denominator ideal, linear
fractional transform, anti-integral element. |
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