ON MODULES WITH THE KULIKOV PROPERTY AND PURE SEMISIMPLE MODULES AND RINGS

[摘要] For an R-module M let sigma[M] denote the category of submodules of M-generated modules. M has the Kulikov property if submodules of pure projective modules in sigma[M] are pure projective. The following is proved: Assume M is a locally noetherian module with the Kulikov property and there are only finitely many simple modules in sigma[M]. Then, for every n is-a-member-of N, there are only finitely many indecomposable modules of length less-than-or-equal-to n in sigma[M]. With our techniques we provide simple proofs for some results on left pure semisimple rings obtained by Prest and Zimmermann-Huisgen and Zimmermann with different methods.

[发布日期] 1991-03-29