The Morita Theorem

Yurij A. Drozd and Vladimir V. Kirichenko
Additional contact information
Yurij A. Drozd: Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics
Vladimir V. Kirichenko: Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics

Chapter 8 in Finite Dimensional Algebras, 1994, pp 135-158 from Springer

Abstract: Abstract In Sect. 2.3 we have noted that modules over a division algebra D and modules over the simple algebra M n (D) are “equally structured”. Results of Sect. 2.6 show that, in general, modules over isotypic semisimple algebras possess the same properties: such modules have isomorphic endomorphism rings, etc. In Sect. 3.5 these results have been extended to projective modules over arbitrary isotypic algebras (Lemma 3.5.5). It turns out that one can remove the requirement of projectivity: All modules over isotypic algebras are equally structured. However, in order to formulate this statement properly, it is necessary to introduce a number of concepts which presently play an important role in various areas of mathematics. Above all, it is the concept of a category and a functor, as well as the notion of an equivalence of categories, which appears to be a mathematical formulation of the expression “equally structured”.

Date: 1994
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-76244-4_8

Ordering information: This item can be ordered from
http://www.springer.com/9783642762444

DOI: 10.1007/978-3-642-76244-4_8

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().