Genel

Zübeyir Türkoğlu, Dokuz Eylül University.
Date: 8th of November, 2022, Tuesday, Time: 13:30 – 15:30.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.

Abstract: In this seminar we will continue to talk about isoartinian, isonoetherian and isosimple modules and rings, see [1]. First we will give characterizations of being right Noetherian ring over semiprime right isoartinian rings. Then we can talk about some open problems. Finally, we will talk about what has been done about these concepts and what we can do.

References

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

Haldun Özgür Bayındır, The University of Haifa.
Date: 6th of February, 2019, Thursday. Time: 11:00 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In algebraic topology we often encounter chain complexes with extra multiplicative structure. For example, the cochain complex of a topological space has what is called the E_∞-algebra structure which comes from the cup product. In this talk I present an idea for studying such chain complexes, E_∞ differential graded algebras (E_∞ DGAs), using stable homotopy theory. Namely, I discuss new equivalences between E_∞ DGAS that are defined using commutative ring spectra.We say E_∞ DGAs are E_∞ topologically equivalent when the corresponding commutative ring spectra are equivalent. Quasi-isomorphic E_∞ DGAs are E_∞ topologically equivalent. However, the examples I am going to present show that the opposite is not true; there are E_∞ DGAs that are E_∞ topologically equivalent but not quasi-isomorphic. This says that between E_∞ DGAs, we have more equivalences than just the quasi-isomorphisms. I also discuss interaction of E_∞ topological equivalences with the Dyer-Lashof operations and cases where E_∞ topological equivalences and quasi-isomorphisms agree.