- m-CANONICAL IDEALS IN SEMIGROUPS
- Kwak, Dong-Je ; Kim, Myeong-Og ; Park, Young-Soo ;
- Bulletin of the Korean Mathematical Society, volume 37, issue 3, 2000, Pages 577~586
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.