October 2022 – Dokuz Eylül University Faculty of Science Department of Mathematics

Zübeyir Türkoğlu, Dokuz Eylül University.
Date: 18th of October, 2022, Tuesday, Time: 13:30 – 14:30.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

Abstract: In this seminar we will talk about isoartinian, isonoetherian and isosimple modules and rings. These notions have been introduced by Facchini and Nazemian in [1]. Let $R$ be a ring. A right $R$ -module $M$ is called isoartinian (isonoetherian) if, for every descending (ascending) chain $M\geq M_1 \geq M_2 \geq …$ ( $M_1 \leq M_2 \leq M_3 \leq …$ ) of submodules of $M$ , there exists an index $n \geq 1$ such that $M_n$ is isomorphic to $M_i$ for every $i\geq n$ . A ring $R$ is called right isoartinian (isonoetherian) if $R_R$ is an isoartinian (isonoetherian) $R$ -module. It is clear from the definitions that right artinian (noethrian) rings are right isoartinian (isonoetherian). We know that right artinian rings are right noetherian. Can we also say that right isoartinian rings are right isonoetherian?

References

[1] A. Facchini and Z. Nazemian, Modules with chain conditions up to isomorphism, Journal of Algebra, pp. 578–601, Vol. 453, 2016.