On the generalization of torsion functor and P-semiprime modules over noncommutative rings
Let R be an associative Noetherian unital noncommutative ring R. We introduce the functor PΓP over the category of R-modules and use it to characterize P-semiprime. P-semisecond R-modules also characterized by the functor PΛP. We also show that the Greenless-May Duality (GM) and Matlis Greenless-May...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Mohaghegh Ardabili
2024-06-01
|
| Series: | Journal of Hyperstructures |
| Subjects: | |
| Online Access: | https://jhs.uma.ac.ir/article_3032_b02124bc63a3058d662ac40248ecb1e4.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Let R be an associative Noetherian unital noncommutative ring R. We introduce the functor PΓP over the category of R-modules and use it to characterize P-semiprime. P-semisecond R-modules also characterized by the functor PΛP. We also show that the Greenless-May Duality (GM) and Matlis Greenless-May Equality(MGM) hold over the full subcategory of R-Mod consisting of R-semiprime and R-semisecond modules. Finally, we generate a one-sided right ideal PΓP(R), which gives an equivalent formulation to solve K{\"o}the conjecture positively or negatively. |
|---|---|
| ISSN: | 2251-8436 2322-1666 |