Math Dept. Seminar - "Ideal Containment in Commutative Rings" - Prof. Abdelslam Mimouni

 

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College of Computing and Mathematics

 

Mathematics Department

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Presents a Seminar

 

"Ideal Containment in Commutative Rings"

 

 

Date: Wednesday, April 12, 2023

Time:  11:00 am

Location: Bldg. 5, Room 103

 

Speaker:

Prof. Abdelslam Mimouni

Professor

Department of Mathematics

College of Computing and Mathematics

KFUPM, Saudi Arabia.

 

Abstract:

Let R be a commutative ring with identity. An ideal I of R is said to be a big ideal (resp. an upper big ideal) if whenever J ⸦ I (resp.,  I ⸦ J), J^{n}⸦ I^{n}$ (resp., I^{n}⸦ J^{n}) for every positive integer n; and R itself is a big ideal ring provided that every ideal of R is a big ideal. In this talk, we will present recent developments of the notions of big ideals, upper big ideals and big ideal rings in different contexts of commutative rings and show that how these notions correlated to some well-known notions such us basic ideals, C-ideals, Ratliff-Rush ideals and more. We give a new characterization of Pr\"ufer domains via big ideal domains.

 

Short bio of presenter:

A. Mimouni is a Professor at KFUPM. His interest is commutative algebra, mainly Multiplicative ideal Theory.

 

 

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All faculty, researchers and graduate students are invited to attend.

 

Department of Mathematics, College of Computing and Mathematics

Telephone: +966 (13) 860 2193, Email: c-math@kfupm.edu.sa,

Website: www.kfupm.edu.sa/departments/math/

 

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