Facchini, Alberto Subdirect representations of categories of modules. (English) Zbl 1196.16002 Dung, Nguyen Viet (ed.) et al., Rings, modules and representations. International conference on rings and things in honor of Carl Faith and Barbara Osofsky, Zanesville, OH, USA, June 15–17, 2007. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4370-3/pbk). Contemporary Mathematics 480, 139-151 (2009). Summary: Let \(R\) be an associative ring with identity. We determine the minimal nonzero ideals of the category \(\text{Mod-}R\), and find a representation of \(\text{Mod-}R\) as a subdirect product of subdirectly irreducible preadditive categories. The category \(\text{Mod-}R\) turns out to be subdirectly irreducible if and only if \(R\) has a unique simple right module up to isomorphism.For the entire collection see [Zbl 1158.16001]. Cited in 1 ReviewCited in 1 Document MSC: 16D90 Module categories in associative algebras 18E05 Preadditive, additive categories 16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras Keywords:subdirect products; preadditive categories; categories of modules; subdirectly irreducible categories; simple modules PDFBibTeX XMLCite \textit{A. Facchini}, Contemp. Math. 480, 139--151 (2009; Zbl 1196.16002)