Decompositions of dual automorphism invariant modules over semiperfect rings
| Autor: | Yosuke Kuratomi |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Endomorphism Direct sum General Mathematics Mathematics::Rings and Algebras 010102 general mathematics Square-free integer Epimorphism Automorphism 01 natural sciences Perfect ring Mathematics::Group Theory 0103 physical sciences 010307 mathematical physics 0101 mathematics Invariant (mathematics) Indecomposable module Mathematics |
| Zdroj: | Sibirskii matematicheskii zhurnal. 60:630-639 |
| ISSN: | 0037-4474 |
| DOI: | 10.33048/smzh.2019.60.311 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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