AGQP-Injective Modules
Let 𝑅 be a ring and let 𝑀 be a right 𝑅-module with 𝑆 = End(𝑀𝑅). 𝑀 is called almost general quasi-principally injective (or AGQP-injective for short) if, for any 0≠𝑠∈𝑆, there exist a positive integer 𝑛 and a left ideal 𝑋𝑠𝑛 of 𝑆 such that 𝑠𝑛≠0 and 𝐥𝑆(Ker(𝑠𝑛))=𝑆𝑠𝑛⊕𝑋𝑠𝑛. Some characterizations and proper...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/469725 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832545272444485632 |
|---|---|
| author | Zhanmin Zhu Xiaoxiang Zhang |
| author_facet | Zhanmin Zhu Xiaoxiang Zhang |
| author_sort | Zhanmin Zhu |
| collection | DOAJ |
| description | Let 𝑅 be a ring and let 𝑀 be a right 𝑅-module with 𝑆 = End(𝑀𝑅). 𝑀 is called almost general quasi-principally injective (or AGQP-injective for short) if, for any 0≠𝑠∈𝑆, there exist a positive integer 𝑛 and a left ideal 𝑋𝑠𝑛
of 𝑆 such that 𝑠𝑛≠0 and 𝐥𝑆(Ker(𝑠𝑛))=𝑆𝑠𝑛⊕𝑋𝑠𝑛. Some characterizations and properties of AGQP-injective modules are given, and some properties of
AGQP-injective modules with additional conditions are studied. |
| format | Article |
| id | doaj-art-edc5ac481485433baa03261d16b7aa07 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-edc5ac481485433baa03261d16b7aa072025-02-03T07:26:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/469725469725AGQP-Injective ModulesZhanmin Zhu0Xiaoxiang Zhang1Department of Mathematics, Jiaxing University, Jiaxing, Zhejiang 314001, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, ChinaLet 𝑅 be a ring and let 𝑀 be a right 𝑅-module with 𝑆 = End(𝑀𝑅). 𝑀 is called almost general quasi-principally injective (or AGQP-injective for short) if, for any 0≠𝑠∈𝑆, there exist a positive integer 𝑛 and a left ideal 𝑋𝑠𝑛 of 𝑆 such that 𝑠𝑛≠0 and 𝐥𝑆(Ker(𝑠𝑛))=𝑆𝑠𝑛⊕𝑋𝑠𝑛. Some characterizations and properties of AGQP-injective modules are given, and some properties of AGQP-injective modules with additional conditions are studied.http://dx.doi.org/10.1155/2008/469725 |
| spellingShingle | Zhanmin Zhu Xiaoxiang Zhang AGQP-Injective Modules International Journal of Mathematics and Mathematical Sciences |
| title | AGQP-Injective Modules |
| title_full | AGQP-Injective Modules |
| title_fullStr | AGQP-Injective Modules |
| title_full_unstemmed | AGQP-Injective Modules |
| title_short | AGQP-Injective Modules |
| title_sort | agqp injective modules |
| url | http://dx.doi.org/10.1155/2008/469725 |
| work_keys_str_mv | AT zhanminzhu agqpinjectivemodules AT xiaoxiangzhang agqpinjectivemodules |