Dean, S. (2019) Duality and contravariant functors in the representation theory of artin algebras. Journal of Algebra and Its Applications, 18(6), 1950111. (doi: 10.1142/s0219498819501111)
|
Text
165713.pdf - Accepted Version 283kB |
Abstract
We know that the model theory of modules leads to a way of obtaining definable categories of modules over a ring R as the kernels of certain functors (R-Mod)op→Ab rather than of functors R-Mod→Ab which are given by a pp-pair. This paper will give various algebraic characterizations of these functors in the case that R is an artin algebra. Suppose that R is an artin algebra. An additive functor G:(R-Mod)op→Ab preserves inverse limits and G|(R-mod)op:(R-mod)op→Ab is finitely presented if and only if there is a sequence of natural transformations (−,A)→(−,B)→G→0 for some A,B∈R-mod which is exact when evaluated at any left R-module. Any additive functor (R-Mod)op→Ab with one of these equivalent properties has a definable kernel, and every definable subcategory of R-Mod can be obtained as the kernel of a family of such functors. In the final section, a generalized setting is introduced, so that our results apply to more categories than those of the form R-Mod for an artin algebra R. That is, our results are extended to those locally finitely presented K-linear categories whose finitely presented objects form a dualizing variety, where K is a commutative artinian ring.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Dean, Mr Samuel |
| Authors: | Dean, S. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal of Algebra and Its Applications |
| Publisher: | World Scientific Publishing |
| ISSN: | 0219-4988 |
| ISSN (Online): | 1793-6829 |
| Published Online: | 18 July 2018 |
| Copyright Holders: | Copyright © 2018 World Scientific Publishing Co Pte Ltd |
| First Published: | First published in Journal of Algebra and Its Applications 18:1950111 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
| Related URLs: |
University Staff: Request a correction | Enlighten Editors: Update this record
Deposit and Record Details
Deposit and Record Details