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Representable Dualities between Finitely Closed Subcategories of Modules

Published online by Cambridge University Press:  20 November 2018

Roderick N. S. MacDonald
Roderick N. S. MacDonald*
Affiliation:
McAlaster University, Hamilton, Ontario
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This paper studies dualities (or contravariant category equivalences) between two categories of R-right and S-left modules which are finitely closed) that is, closed under submodules, factor modules and finite direct sums. Omitting the requirement that the categories contain all finitely generated modules from the classical Morita situation provides a generalization which substantially increases the number of such dualities.

We prove that a duality between two finitely closed categories A and B of modules is representable if and only if A and B consist of linearly compact modules. This encompasses work of Mueller ([7], [8]) for Morita dualities and of Goblot ([5], [6]).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 3 , 01 June 1979 , pp. 465 - 475
Copyright
Copyright © Canadian Mathematical Society 1979

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