2025/07/15 by S. D. Dubey, Kriti Goel, Dubey, Saipriya +7 · 3 citations
Computer Science · #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2507.11738
openalex publication_date 2025/07/15 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
Judith Sally proved in 1980 that the associated graded ring of one-dimensional Gorenstein local rings of multiplicity e and embedding dimension e-2 are Cohen-Macaulay. She showed that the defining ideal of the associated graded ring of such rings is generated by e-2 \choose 2 elements. Numerical semigroup rings are a big class of one-dimensional Cohen-Macaulay rings. In 2014, Herzog and Stamate proved that the numerical semigroup defines a Gorenstein semigroup ring satisfying Sally's conditions above and such semigroups are called Gorenstein Sally Semigroups. We call a numerical semigroup S as Sally type if = < e,e+1,…,e+m-1, e+m+1,…, e+n-1,e+n+1, … 2e-1> for some 2 ≤ m