ROOM 7: Isomorphisms and extensions of uniserial modules

Abstract: The first open problems in Auslander - Reiten - Smalo book " Representation Theory of Artin algebras " deal with uniserial modules. In particular Problem 1 deals with the isomorphism problem for uniserial modules, while Problem 3 deals with the extension problem for the same modules. I will present a partial solution to Problems 1 and 3 obtained in two joint papers with Fatma Kaynarca and Derya Keskin Tutuncu. Concerning the isomorphism problem, we obtain a " two fixed point theorem" . Finally, concerning the extension problem we obtain a " two terms in the middle theorem" . Google and the words " Isomorphism problem for uniserial modules over arbitrary rings " give the file of our first paper in Comm. Algebra (April 2020). Google and the words " Forthcoming articles, Mathematics, Padova " give the link to our second paper " Extensions of uniserial modules " , acceped for publication in Rendiconti del Seminario Matematico dell'Università di Padova.

combinatoricscategory theoryrings and algebrasrepresentation theory

Audience: researchers in the topic

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Sherbrooke Meeting on Representation Theory of Algebras, Corona Edition (fully online)

Series comments: Please contact Thomas Brüstle or Juan Carlos Bustamante if you are interested to participate.