|
Zapiski Nauchnykh Seminarov POMI, 2001, Volume 281, Pages 186–209
(Mi znsl1495)
|
|
|
|
This article is cited in 1 scientific paper (total in 1 paper)
Continuous functors and duality
M. B. Zvyagina Saint-Petersburg State University
Abstract:
Let $\Lambda$ be an associative ring with unity and let ${}_\Lambda\mathfrak M$ be a category of left unitary $\Lambda$-modules. The complete characterization of continuous additive co- and contravariant functors ${}_\Lambda\mathfrak M\to_\mathbb Z\mathfrak M$ is given. Such functors are either representable, or equivalent to a tenzor product, or the trivial functor. The class of categories, which are dual to ${}_\Lambda\mathfrak M$ and thefore equivalent to the category of compact right $\Lambda$-modules, is constructed by purely algebraic means. The canonical category is extracted from this class. The purely algebraic structure is constructed that is equivalent to the topology-algebraic structure of compact right $\Lambda$-module. Algebraic equivalents of connectivity and of complete inconnectivity are given.
Received: 21.06.2001
Citation:
M. B. Zvyagina, “Continuous functors and duality”, Problems in the theory of representations of algebras and groups. Part 8, Zap. Nauchn. Sem. POMI, 281, POMI, St. Petersburg, 2001, 186–209; J. Math. Sci. (N. Y.), 120:4 (2004), 1591–1602
Linking options:
https://www.mathnet.ru/eng/znsl1495 https://www.mathnet.ru/eng/znsl/v281/p186
|
Statistics & downloads: |
Abstract page: | 145 | Full-text PDF : | 52 |
|