Thesis supervisor: Gábor Czédli
Location of studies (in Hungarian): SZTE TTIK Matematika- és Számítástudományok Doktori Iskola 6720 Szeged, Aradi vértanúk tere 1. Abbreviation of location of studies: MatDI
Description of the research topic:
Both lattices and categories are mathematical tools that make it possible to eliminate calculations with concrete elements, whereby they can point out the real reasons of some mathematical theorems. It is not surprising that there are serious connections between these two tools. The aim of the present topic is to study these connections and developing earlier results further. Emphasis is given to the following two research fields. The first one is based on a theorem of Hutchinson asserting that the study of the existence of exact embedding functors between (Abelian) categories of modules is equivalent to the study of the inclusion relation between the corresponding quasivarieties of submodule lattices; the concrete task is to give lattice theoretical proofs for some results proved earlier with the toolkit of abelian categories. The second one is based on some results of Marcel Erné (in part, joint with the suprevisor), which says that some closure operators formulated for categories can naturally be defined for algebraic (and even for continuous) lattices.
Further requirements: Mathematical creativity and experience with rigorous proofs in algebra
Number of students who can be accepted: 1
Deadline for application: 2017-09-01
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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