All 𝑛-cotilting modules are pure-injective

Šťovíček, Jan

doi:10.1090/S0002-9939-06-08256-6

All $n$-cotilting modules are pure-injective
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Proc. Amer. Math. Soc. 134 (2006), 1891-1897 Request permission

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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