Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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m-CANONICAL IDEALS IN SEMIGROUPS

  • Kwak, Dong-Je (Department of Mathematics, Kyungpook National University) ;
  • Kim, Myeong-Og (Department of Mathematics, Kyungpook National University) ;
  • Park, Young-Soo (Department of Mathematics, Kyungpook National University)
  • Published : 2000.08.01
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Abstract

For a grading monoid S, we prove that (1) if (S, M) is a valuation semigroup, then M is an m-canonical ideal, that is, an ideal M such that M : (M:J)=J for every ideal J of S. (2) if S is an integrally closed semigroup and S has a principal m-canonical ideal, then S is a valuation semigroup, and (3) if S is a completely integrally closed and S has an m-canonical ideal I, then every ideal of S is I-invertible, that is, J+(I+J)=I for every ideal J of S.

Keywords

References

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