Exploring EADS Modules: Properties, Direct Sums, and Applications in Matrix Rings
We introduce the concept of an EADS module, defined such that for any decomposition M=A⊕B and any ec-complement C of A in M, the module satisfies M=A⊕C. This study explores the properties of EADS modules and examines their relationships with other established properties. We particularly investigate...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/9159580 |
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| _version_ | 1832568858721910784 |
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| author | Farnaz Davachi Miandouab Canan Celep Yücel |
| author_facet | Farnaz Davachi Miandouab Canan Celep Yücel |
| author_sort | Farnaz Davachi Miandouab |
| collection | DOAJ |
| description | We introduce the concept of an EADS module, defined such that for any decomposition M=A⊕B and any ec-complement C of A in M, the module satisfies M=A⊕C. This study explores the properties of EADS modules and examines their relationships with other established properties. We particularly investigate the behavior of EADS modules concerning direct sums and direct summands. In addition, we present applications, including matrix rings over a right EADS ring. |
| format | Article |
| id | doaj-art-9522bb65859d4bef874ed09739555d19 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-9522bb65859d4bef874ed09739555d192025-02-03T00:12:25ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/9159580Exploring EADS Modules: Properties, Direct Sums, and Applications in Matrix RingsFarnaz Davachi Miandouab0Canan Celep Yücel1Department of MathematicsDepartment of MathematicsWe introduce the concept of an EADS module, defined such that for any decomposition M=A⊕B and any ec-complement C of A in M, the module satisfies M=A⊕C. This study explores the properties of EADS modules and examines their relationships with other established properties. We particularly investigate the behavior of EADS modules concerning direct sums and direct summands. In addition, we present applications, including matrix rings over a right EADS ring.http://dx.doi.org/10.1155/2024/9159580 |
| spellingShingle | Farnaz Davachi Miandouab Canan Celep Yücel Exploring EADS Modules: Properties, Direct Sums, and Applications in Matrix Rings Journal of Mathematics |
| title | Exploring EADS Modules: Properties, Direct Sums, and Applications in Matrix Rings |
| title_full | Exploring EADS Modules: Properties, Direct Sums, and Applications in Matrix Rings |
| title_fullStr | Exploring EADS Modules: Properties, Direct Sums, and Applications in Matrix Rings |
| title_full_unstemmed | Exploring EADS Modules: Properties, Direct Sums, and Applications in Matrix Rings |
| title_short | Exploring EADS Modules: Properties, Direct Sums, and Applications in Matrix Rings |
| title_sort | exploring eads modules properties direct sums and applications in matrix rings |
| url | http://dx.doi.org/10.1155/2024/9159580 |
| work_keys_str_mv | AT farnazdavachimiandouab exploringeadsmodulespropertiesdirectsumsandapplicationsinmatrixrings AT canancelepyucel exploringeadsmodulespropertiesdirectsumsandapplicationsinmatrixrings |