Abstract
For an artin algebra A we show that maximal submodules of pure-projective right A-modules (i.e. of direct sums of finitely generated A-modules) are again pure-projective if and only if A is of finite representation type. More generally we show that a right artinian ring A, such that the injective hulls of finitely generated right A-modules are finitely generated, is right pure-semisimple if and only if maximal submodules of pure-projective right A-modules are pure-projective.
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© 1980 Springer-Verlag
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Brune, H. (1980). On finite representation type and a theorem of Kulikov. In: Dlab, V., Gabriel, P. (eds) Representation Theory II. Lecture Notes in Mathematics, vol 832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088462
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DOI: https://doi.org/10.1007/BFb0088462
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