JP Journal of Algebra, Number Theory and Applications
Volume 2, Issue 2, Pages 101 - 109
(August 2002)
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ON SEMIGROUPS WHICH HAVE PRIME IDEALS THAT ARE LINEARLY
ORDERED
Mitsuo Kanemitsu (Japan), Kentaro Hatano (Japan) and Mamoru Furuhata (Japan)
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Abstract: Let G be
a torsion-free additive group and let S be a
submonoid of G. If S is a
GCD-semigroup which has prime ideals that are
linearly ordered, then S is a valuation
semigroup. Furthermore, we give characterizations of
divided semigroups. Also, we give characterizations
of pseudo-valuation semigroups. |
Keywords and phrases: valuation semigroup, GCD-semigroup, pseudo-valuation semigroup,
divided semigroup. |
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