JP Journal of Algebra, Number Theory and Applications
Volume 3, Issue 3, Pages 377 - 389
(December 2003)
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THE IDEAL TRANSFORMS
OF SEMIGROUPS
Mitsuo Kanemitsu (Japan)
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Abstract: Let S be
a submonoid of a torsion-free abelian (additive)
group G. Let Space(S).
be the set of all prime ideals of S and
let I be an ideal of S. We study
some properties of the Kaplansky ideal transform
WS(I)
and
Nagata ideal transform TS(I).
In particular, we give the equivalent condition
to I
+ WS
(I) = I. Also we consider WS(I)
and TS(I)
of S
= Z0 U
(Z + Z1X)
which are valuation semigroups of dimension two. |
Keywords and phrases: valuation
semigroup, ideal transform, flat oversemigroup. |
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