Siberian Mathematical Journal

, Volume 60, Issue 3, pp 490–496 | Cite as

Decompositions of Dual Automorphism Invariant Modules over Semiperfect Rings

  • Y. KuratomiEmail author


A module M is called dual automorphism invariant if whenever X1 and X2 are small submodules of M, then each epimorphism f : M/X1M/X2 lifts to an endomorphism g of M. A module M is said to be d-square free (dual square free) if whenever some factor module of M is isomorphic to N2 for a module N then N = 0. We show that each dual automorphism invariant module over a semiperfect ring which is a small epimorphic image of a projective lifting module is a direct sum of cyclic indecomposable d-square free modules. Moreover, we prove that for each module M over a semiperfect ring which is a small epimorphic image of a projective lifting module (e.g., M is a finitely generated module), M is dual automorphism invariant iff M is pseudoprojective. Also, we give the necessary and sufficient conditions for a dual automorphism invariant module over a right perfect ring to be quasiprojective.


dual automorphism invariant module pseudoprojective module dual square free module finite internal exchange property (semi)perfect ring 


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Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceYamaguchi UniversityYoshida, YamaguchiJapan

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