21 SEP 2023
10:00 - 12:00

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 been very intense in the last years. There are several different ways to approach this study. One of them was recently initiated by Herzog, Hibi, and Stamate in [2] introducing the notion of nearly Gorenstein ring. A Cohen-Macaulay local ring $R$ admitting a canonical module $omega_R$ is said to be nearly Gorenstein if $ r(omega_R)$ contains the maximal ideal (there is a similar notion for positively graded algebras over a field). In these talks, we study the trace ideal of semidualizing modules, give some characterizations of them and compare them with annihilators of specific Ext modules. Then, two new classes of rings, namely quasi nearly Gorenstein and weakly nearly Gorenstein, are introduced as generalizations of nearly Gorenstein rings; [1].
references:
1. M. Bagherpoor and A. Taherizadeh. Trace ideals of semidualizing modules and two generalizations of nearly Gorenstein rings, Communications in Algebra {51}(2) (2023), 446-463.
2. J. Herzog, T. Hibi, and D. I. Stamate. The trace of the canonical module. Isr. J. Math. 233 (2019), 133-165.
3. H. Lindo, Trace ideals and centers of endomorphism rings of modules over commutative rings, Journal of Algebra {482} (2017), 102-130.
online in Zoom: https://zoom.us/join
Meeting ID: 9086116889
Passcode: 362880
Venue: Niavaran, Lecture Hall 2

21 SEP 2023
11:00 - 12:00

Abstract:

Inertia is the intrinsic tendency of matter to remain in a given condition. The state of a particle in spacetime is determined by its mass and spin, which characterize the irreducible unitary representations of the inhomogeneous Lorentz group. Therefore, the inertial attributes of a particle are determined by its mass and spin. The inertial properties of mass are well known; hence, I concentrate on the inertial properties of intrinsic spin.

Meeting Place:
Seminar Room, School of Particles and Accelerators, IPM

15 NOV 2023
-

Date: 15-17 November 2023

Link: https://physics.ipm.ac.ir/conferences/ishep/index.jsp

16 NOV 2023
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Date: 15-17 November 2023

Link: https://physics.ipm.ac.ir/conferences/ishep/index.jsp

17 NOV 2023
-

Date: 15-17 November 2023

Link: https://physics.ipm.ac.ir/conferences/ishep/index.jsp