[Turkmath:2517] Hacettepe Uni. Dept. of Mathematics General Seminar by Toma Albu -15 Sept

[Oğuz Yayla]

Hacettepe University
Department of Mathematics

GENERAL SEMINAR

Yaşar Ataman Seminar Room, 15 September 2017; 11:00

There will be some refreshments before the talk.


*The Osofsky-Smith Theorem in rings, modules, categories, torsion theories,
and lattices*

by

*TOMA ALBU*

Simion Stoilow Institute of Mathematics
of the Romanian Academy, Bucharest, Romania

The renown Osofsky-Smith Theorem (O-ST), invented in 1991, says that a
cyclic
(finitely generated) right R-module such that all of its cyclic (finitely
generated) sub-
factors are CS modules is a finite direct sum of uniform submodules.

In this talk we present various extensions of this theorem to Grothendieck
categories
(the Categorical O-ST), module categories equipped with a hereditary
torsion theory
(the Relative O-ST), and modular lattices (the Latticial O-ST); it
illustrates a general
strategy which consists on putting a module-theoretical concept/result into
a latticial
frame (we call it latticization) in order to translate that concept/result
to Grothendieck
categories (we call it absolutization) and module categories equipped with
a hereditary
torsion theorie (we call it relativization).
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