On Almost Projective Modules
In this note, we investigate the relationship between almost projective modules and generalized projective modules. These concepts are useful for the study on the finite direct sum of lifting modules. It is proved that; if <i>M</i> is generalized <i>N</i>-projective for any m...
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2021-02-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/1/21 |
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doaj-12a3b54597d340a89ac5c62008f767832021-02-17T00:00:22ZengMDPI AGAxioms2075-16802021-02-0110212110.3390/axioms10010021On Almost Projective ModulesNil Orhan Ertaş0Department of Mathematics, Bursa Technical University, Bursa 16330, TurkeyIn this note, we investigate the relationship between almost projective modules and generalized projective modules. These concepts are useful for the study on the finite direct sum of lifting modules. It is proved that; if <i>M</i> is generalized <i>N</i>-projective for any modules <i>M</i> and <i>N</i>, then <i>M</i> is almost <i>N</i>-projective. We also show that if <i>M</i> is almost <i>N</i>-projective and <i>N</i> is lifting, then <i>M</i> is im-small <i>N</i>-projective. We also discuss the question of when the finite direct sum of lifting modules is again lifting.https://www.mdpi.com/2075-1680/10/1/21generalized projective modulealmost projective modules |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Nil Orhan Ertaş |
| spellingShingle |
Nil Orhan Ertaş On Almost Projective Modules Axioms generalized projective module almost projective modules |
| author_facet |
Nil Orhan Ertaş |
| author_sort |
Nil Orhan Ertaş |
| title |
On Almost Projective Modules |
| title_short |
On Almost Projective Modules |
| title_full |
On Almost Projective Modules |
| title_fullStr |
On Almost Projective Modules |
| title_full_unstemmed |
On Almost Projective Modules |
| title_sort |
on almost projective modules |
| publisher |
MDPI AG |
| series |
Axioms |
| issn |
2075-1680 |
| publishDate |
2021-02-01 |
| description |
In this note, we investigate the relationship between almost projective modules and generalized projective modules. These concepts are useful for the study on the finite direct sum of lifting modules. It is proved that; if <i>M</i> is generalized <i>N</i>-projective for any modules <i>M</i> and <i>N</i>, then <i>M</i> is almost <i>N</i>-projective. We also show that if <i>M</i> is almost <i>N</i>-projective and <i>N</i> is lifting, then <i>M</i> is im-small <i>N</i>-projective. We also discuss the question of when the finite direct sum of lifting modules is again lifting. |
| topic |
generalized projective module almost projective modules |
| url |
https://www.mdpi.com/2075-1680/10/1/21 |
| work_keys_str_mv |
AT nilorhanertas onalmostprojectivemodules |
| _version_ |
1724265864991080448 |