Commutative Algebra Seminar
Speaker: Om Prakash
Affiliation: IIT Bombay
Host: Tony J. Puthenpurakal
Time: Tuesday, 16 April 2024, 4:00-5:00 pm
Venue: Room # 215
Title: Commutative Algebra Seminar
Title: Numerical Semigroups and associated Semigroup Rings-II.
Abstract: In this series of two lectures, we will study numerical
semigroups and their associated semigroup rings. Initially, we will define
numerical
semigroups, state their fundamental properties, and introduce relevant
invariants. Subsequently, we aim to prove the following fundamental
results: (i) The Frobenius number of a numerical semigroup S equals the
degree, viewed as a rational function, of the Hilbert series of the
numerical semigroup ring k[S]. (ii) The Cohen-Macaulay type of the
numerical semigroup ring k[S] corresponds to the number of
pseudo-Frobenius elements of S. Consequently, we derive a well-known
result concerning Gorenstein numerical semigroup rings (credited to
Kunz) asserting that k[S] is Gorenstein if and only if S is symmetric.