2023/04/28 by Om Prakash Bhardwaj, Bhardwaj, Om Prakash, Indranath Sengupta +1 · 1 citation
Mathematics · #13A02 #13D02 #20M14 #20M25 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2304.14806
openalex publication_date 2023/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If the Krull dimension of the semigroup ring is greater than one, then affine semigroups of maximal projective dimension (MPD) are not Cohen-Macaulay, but they may be Buchsbaum. We give a necessary and sufficient condition for simplicial MPD-semigroups to be Buchsbaum in terms of pseudo-Frobenius elements. We give certain characterizations of \prec-almost symmetric C-semigroups. When the cone is full, we prove the irreducible C-semigroups, and \prec-almost symmetric C-semigroups with Betti-type three satisfy the extended Wilf's conjecture. For e ≥ 4, we give a class of MPD-semigroups in ℕ2 such that there is no upper bound on the Betti-type in terms of embedding dimension e. Thus, the Betti-type may not be a bounded function of the embedding dimension. We further explore the submonoids of ℕd, which satisfy the Arf property.