2023/05/31 by Endo, Naoki
#Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2305.19633
For an Ulrich ideal in a Gorenstein local ring, the quotient ring is again Gorenstein. Aiming to further develop the theory of Ulrich ideals, this paper investigates a naive question of how many non-principal ideals whose quotient rings are Gorenstein exist in a given Gorenstein ring. The main result provides that the number of such graded ideals in a symmetric numerical semigroup ring R coincides with the conductor of the semigroup. We furthermore provide a complete list of non-principal graded ideals I in R whose quotient rings R/I are Gorenstein.