October 30, 2020
4:10PM - 5:10PM
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2020-10-30 16:10:00
2020-10-30 17:10:00
Ring Theory Seminar - André Leroy
Title: Commutatively closed sets and their graphs
Speaker: André Leroy - Universite Artois, Lens, France
Abstract: The notion of commutatively closed subsets was introduced in 2017 as a way of generalizing different kinds of rings such as Dedekind finite, reversible, semicommutative rings. A subset S of a ring R is commutatively closed if whenever a product ab is in S then ba is also in S. Any subset S can be embedded in a subset T which is commutatively closed. After giving quite a few examples, we will characterize a few types of elements that are commutatively closed. We will also mention some connections with the left and right annihilators and mention some subsets of a ring that are always commutatively closed. A natural topology will emerge as well as a graph. We will define the diameter of a ring and compute the diameter of any Artinian semisimple algebra. At the end of the talk, we will mention a few open problems.
This is a joint work with D. Alghazzawi (Saudi Arabia) and M. Abdi (Iran)
Seminar Zoom Link
Meeting ID: 927 3710 0856 Password: 694623
Zoom Link: see event
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Add to Calendar
2020-10-30 16:10:00
2020-10-30 17:10:00
Ring Theory Seminar - André Leroy
Title: Commutatively closed sets and their graphs
Speaker: André Leroy - Universite Artois, Lens, France
Abstract: The notion of commutatively closed subsets was introduced in 2017 as a way of generalizing different kinds of rings such as Dedekind finite, reversible, semicommutative rings. A subset S of a ring R is commutatively closed if whenever a product ab is in S then ba is also in S. Any subset S can be embedded in a subset T which is commutatively closed. After giving quite a few examples, we will characterize a few types of elements that are commutatively closed. We will also mention some connections with the left and right annihilators and mention some subsets of a ring that are always commutatively closed. A natural topology will emerge as well as a graph. We will define the diameter of a ring and compute the diameter of any Artinian semisimple algebra. At the end of the talk, we will mention a few open problems.
This is a joint work with D. Alghazzawi (Saudi Arabia) and M. Abdi (Iran)
Seminar Zoom Link
Meeting ID: 927 3710 0856 Password: 694623
Zoom Link: see event
Department of Mathematics
math@osu.edu
America/New_York
public
Title: Commutatively closed sets and their graphs
Speaker: André Leroy - Universite Artois, Lens, France
Abstract: The notion of commutatively closed subsets was introduced in 2017 as a way of generalizing different kinds of rings such as Dedekind finite, reversible, semicommutative rings. A subset S of a ring R is commutatively closed if whenever a product ab is in S then ba is also in S. Any subset S can be embedded in a subset T which is commutatively closed. After giving quite a few examples, we will characterize a few types of elements that are commutatively closed. We will also mention some connections with the left and right annihilators and mention some subsets of a ring that are always commutatively closed. A natural topology will emerge as well as a graph. We will define the diameter of a ring and compute the diameter of any Artinian semisimple algebra. At the end of the talk, we will mention a few open problems.
This is a joint work with D. Alghazzawi (Saudi Arabia) and M. Abdi (Iran)
Meeting ID: 927 3710 0856 Password: 694623