On Isoartinian and Isonoetherian Modules

Hakan Şanal, Dokuz Eylül University.
Date: 22nd of May, 2019, Wednesday. Time: 14:30 – 16:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In [1, 2], Facchini and Nazemian generalize the idea of Artinian and Noetherian modules by considering the chain conditions up to isomorphism. They call a module M isoartinan (resp. isonoetherian) if, for every descending (resp. ascending) chain M ≥ M1 ≥ M2 ≥ · · · (resp. M1 ≤ M2 ≤ M3 ≤ · · · ) of submodules of M , there exists an index n ≥ 1 s.t. Mn Mi for every i ≥ n. Similarly, M is called isosimple if M is non-zero and every non-zero submodule of M is isomorphic to M. In this seminar, we will give some properties of these three classes of modules.
[1] A. Facchini and Z. Nazemian, Modules with chain conditions up to isomorphism. J. Algebra 453 (2016): 578–601.
[2] A. Facchini and Z. Nazemian, Artinian dimension and isoradical of modules. J. Algebra 484 (2017): 66–87.