A local duality theorem for categories of modules

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.