NOTE ON 1-DIMENSIONAL INTEGRALLY CLOSED MORI SEMIGROUPS

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Published: Dec 1, 1999
DOI: https://doi.org/10.5556/j.tkjm.30.1999.4235
Keywords:
Mori semigroup valuation semigroup

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YOSHIKO KITSUNEZUKA
Department of Mathematics, Toyama University, Gofuku, Toyama 930, Japan
RYUKI MATSUDA
Department of Mathematical Sciences, Ibaraki University, Mito, Ibaraki 310, Japan.
TAKASI SUGATANI
Department of Mathematics, Toyama University, Gofuku, Toyama 930, Japan.

Abstract




We show that a I-dimensional integrally closed quasi-local Mori semi-group need not be a valuation semigroup, which is a negative answer to a sem1group version of the question of Querre.




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How to Cite
KITSUNEZUKA, Y., MATSUDA, R., & SUGATANI, T. (1999). NOTE ON 1-DIMENSIONAL INTEGRALLY CLOSED MORI SEMIGROUPS. Tamkang Journal of Mathematics, 30(4), 295–297. https://doi.org/10.5556/j.tkjm.30.1999.4235
Issue
Vol. 30 No. 4 (1999)
Section
Papers
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References

V. Barucci, On a class of Mori domains, Comm. Alg. 11(1983), 1989-2001

R. Gilmer, Commutative Semigroup Rings, Univ. Chicago Press, 1984.

R. Matsuda, On some properties between rings and semigroups, Math. J. Ibaraki Uinv. 29(1997), 9-23.

J. Querre, Sur une propriete des anneaux de Krull, Bull. Sci. Math. 95(1971), 341-354.