Decompositions of Dual Automorphism Invariant Modules over Semiperfect Rings
- Authors: Kuratomi Y.1
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Affiliations:
- Department of Mathematics, Faculty of Science
- Issue: Vol 60, No 3 (2019)
- Pages: 490-496
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/172427
- DOI: https://doi.org/10.1134/S003744661903011X
- ID: 172427
Cite item
Abstract
A module M is called dual automorphism invariant if whenever X1 and X2 are small submodules of M, then each epimorphism f : M/X1 → M/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.
About the authors
Y. Kuratomi
Department of Mathematics, Faculty of Science
Author for correspondence.
Email: kuratomi@yamaguchi-u.ac.jp
Japan, Yoshida, Yamaguchi