Abstract
We provide a generalization of pseudo-Frobenius numbers of numerical semigroups to the context of the simplicial affine semigroups. In this way, we characterize the Cohen-Macaulay type of the simplicial affine semigroup ring K [ S ] . We define the type of S , type ( S ) , in terms of some Apéry sets of S and show that it coincides with the Cohen-Macaulay type of the semigroup ring, when K [ S ] is Cohen-Macaulay. If K [ S ] is a d -dimensional Cohen-Macaulay ring of embedding dimension at most d + 2 , then type ( S ) ≤ 2 . Otherwise, type ( S ) might be arbitrary large and it has no upper bound in terms of the embedding dimension. Finally, we present a generating set for the conductor of S as an ideal of its normalization.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.