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.
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The authors would like to thank the referee for his/her critical remark. The second author would like to thank CSIR, India for a fellowship.
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KESHARI, M.K., SARWAR, H.P. Serre dimension of monoid algebras. Proc Math Sci 127, 269–280 (2017). https://doi.org/10.1007/s12044-016-0310-7
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DOI: https://doi.org/10.1007/s12044-016-0310-7