Morita Theory

Postgraduate Thesis uoadl:2942539 173 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2021-04-08
Year:
2021
Author:
Xepapadakou Panagiota
Supervisors info:
Εμμανουήλ Ιωάννης, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Κοντογεώργης Αριστείδης, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Ντόκας Ιωάννης, Επίκουρος Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
ΘΕΩΡΙΑ MORITA
Languages:
Greek
Translated title:
Morita Theory
Summary:
A natural question concerning rings is: do the modules of a ring contain all the
information about the structure of that ring? The answer to this question is “no.” This
leads to a new sense of “equivalence” of rings which is coarser than isomorphism. That
is, two rings are “equivalent” when their categories of modules are equivalent (in the
category-theoretical sense). Japanese mathematician Kiiti Morita is known for having
stated and proved theorems which gave an equivalent conditions for this equivalence which, in his honour, have been dubbed “Morita equivalence.”
In this thesis we begin by reviewing the material necessary to define Morita equivalence. Next, we continue by delving in what is called "Morita Theory", which consists from basic theorems of Morita as also some of their consequences. Finally, we move on defining and studing some essential results on duality between module categories, which concern the expression of Morita equality under contravariant functors.
Main subject category:
Science
Keywords:
Morita equivalence, Morita duality, module category
Index:
Yes
Number of index pages:
2
Contains images:
Yes
Number of references:
2
Number of pages:
79
File:
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