| Saturday 7 June 2025 | |
| Events for day: Thursday 21 September 2023 |
| 10:00 - 12:00 Commutative Algebra Seminar Trace Ideals, Nearly Gorenstein Rings and their Generalizations School MATHEMATICS Let $R$ be a commutative Noetherian ring and $M$ be an $R$-module. The trace of $M$, denoted by $ r_R(M)$, is defined as the sum of ideals $phi(M)$, where the sum is taken over all $R$-module homomorphisms $phi:Mlongrightarrow R$. The trace of a module have been considered in various contexts, in particular to better understand the center of the ring of endomorphisms of a module. When the canonical module $omega_R$ of $R$ exists, the significance of the trace of $omega_R$ arises from the fact that it describes the non-Gorenstein locus of $R$. The study of commutative rings lying between Gorenstein and Cohen-Macaulay rings has bee ... |