An Equivalent Condition and Some Properties of Strong J-Symmetric Ring
Let JR denote the Jacobson radical of a ring R. We say that ring R is strong J-symmetric if, for any a,b,c∈R, abc∈JR implies bac∈JR. If ring R is strong J-symmetric, then it is proved that Rx/xn is strong J-symmetric for any n≥2. If R and S are rings and WSR is a R,S-bimodule, E=TR,S,W=RW0S=rw0s|r∈R...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/7335202 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832566383554068480 |
|---|---|
| author | Shun Xu |
| author_facet | Shun Xu |
| author_sort | Shun Xu |
| collection | DOAJ |
| description | Let JR denote the Jacobson radical of a ring R. We say that ring R is strong J-symmetric if, for any a,b,c∈R, abc∈JR implies bac∈JR. If ring R is strong J-symmetric, then it is proved that Rx/xn is strong J-symmetric for any n≥2. If R and S are rings and WSR is a R,S-bimodule, E=TR,S,W=RW0S=rw0s|r∈R,w∈W,s∈S,then it is proved that R and S are J-symmetric if and only if E is J-symmetric. It is also proved that R and S are strong J-symmetric if and only if E is strong J-symmetric. |
| format | Article |
| id | doaj-art-008cc66b6acd462f8f2551cd740d5119 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-008cc66b6acd462f8f2551cd740d51192025-02-03T01:04:17ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/73352027335202An Equivalent Condition and Some Properties of Strong J-Symmetric RingShun Xu0School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, ChinaLet JR denote the Jacobson radical of a ring R. We say that ring R is strong J-symmetric if, for any a,b,c∈R, abc∈JR implies bac∈JR. If ring R is strong J-symmetric, then it is proved that Rx/xn is strong J-symmetric for any n≥2. If R and S are rings and WSR is a R,S-bimodule, E=TR,S,W=RW0S=rw0s|r∈R,w∈W,s∈S,then it is proved that R and S are J-symmetric if and only if E is J-symmetric. It is also proved that R and S are strong J-symmetric if and only if E is strong J-symmetric.http://dx.doi.org/10.1155/2021/7335202 |
| spellingShingle | Shun Xu An Equivalent Condition and Some Properties of Strong J-Symmetric Ring Journal of Mathematics |
| title | An Equivalent Condition and Some Properties of Strong J-Symmetric Ring |
| title_full | An Equivalent Condition and Some Properties of Strong J-Symmetric Ring |
| title_fullStr | An Equivalent Condition and Some Properties of Strong J-Symmetric Ring |
| title_full_unstemmed | An Equivalent Condition and Some Properties of Strong J-Symmetric Ring |
| title_short | An Equivalent Condition and Some Properties of Strong J-Symmetric Ring |
| title_sort | equivalent condition and some properties of strong j symmetric ring |
| url | http://dx.doi.org/10.1155/2021/7335202 |
| work_keys_str_mv | AT shunxu anequivalentconditionandsomepropertiesofstrongjsymmetricring AT shunxu equivalentconditionandsomepropertiesofstrongjsymmetricring |