A local duality theorem for categories of modules
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 4, Tome 227 (1995), pp. 66-73
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Let $\Lambda$ be an associative ring with identity and let $_\Lambda\mathfrak M$ be the category of left unitary $\Lambda$-modules. A subcateqory $\mathcal M$ of the category $_\Lambda\mathfrak M$ is said to be small if the pairwise nonisomorphic objects of $\mathcal M$ form a set. The main result of this paper consists of the fact that for every small full subcategory $\mathcal M$, there exists a ring $\Gamma$ such that $\mathcal M$ is dual to a small full subcategory of the category $_\Gamma\mathfrak M$. Some applications of this result are indicated. Bibliography: 3 titles.
@article{ZNSL_1995_227_a8,
author = {M. B. Zvyagina},
title = {A local duality theorem for categories of modules},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {66--73},
publisher = {mathdoc},
volume = {227},
year = {1995},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1995_227_a8/}
}
M. B. Zvyagina. A local duality theorem for categories of modules. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 4, Tome 227 (1995), pp. 66-73. http://geodesic.mathdoc.fr/item/ZNSL_1995_227_a8/