JP Journal of Algebra, Number Theory and Applications
Volume 1, Issue 1, Pages 25 - 39
(April 2001)
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ON
SEMINORMAL SEMIGROUPS AND PSEUDO-VALUATION
SEMIGROUPS
Mitsuo Kanemitsu (Japan) and Ryûki Matsuda (Japan)
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Abstract: Let G be a
torsion-free commutative (additive) group and S
be a submonoid of G with the quotient
group G. We study some properties of
seminormal semigroups of dimension one. For
example, we show that if S is a
seminormal semigroup of dimension one, then S
is a pseudo-valuation semigroup if and only if
the integral closure
of S is a pseudo-valuation semigroup.
Also, we find that if S is a Noetherian
semigroup, then each oversemigroup of S
is seminormal if and only if S is
seminormal and dim |
Keywords and phrases: seminormal
semigroup, valuation semigroup, pseudo-valuation semigroup,
integral semigroup. |
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