Abstract
Let R be a commutative Noetherian ring of dimension d, M a commutative cancellative torsion-free monoid of rank r and P a finitely generated projective R[M]-module of rank t. Assume M is Φ-simplicial seminormal. If $M\in \mathcal {C}({\Phi })$ , then Serre dim R[M]≤d. If r≤3, then Serre dim R[int(M)]≤d. If $M\subset \mathbb {Z}_{+}^{2}$ is a normal monoid of rank 2, then Serre dim R[M]≤d. Assume M is c-divisible, d=1 and t≥3. Then P≅∧ t P⊕R[M] t−1. Assume R is a uni-branched affine algebra over an algebraically closed field and d=1. Then P≅∧ t P⊕R[M] t−1.
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.