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All -cotilting modules are pure-injective
Authors:Jan Stoví  cek
Institution:Faculty of Mathematics and Physics, Department of Algebra, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
Abstract:We prove that all $ n$-cotilting $ R$-modules are pure-injective for any ring $ R$ and any $ n \ge 0$. To achieve this, we prove that $ {^{\perp_1} U}$ is a covering class whenever $ U$ is an $ R$-module such that $ {^{\perp_1} U}$ is closed under products and pure submodules.

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