The Source of Primeness of Rings
In this study, we define a new concept, i.e., source of primeness of a ring $R$, as $P_{R} := \bigcap_{a\in R} S_{R}^{a}$ such that $S_{R}^{a}:=\{b\in R \mid aRb=(0)\}$. We then examine some basic properties of $P_{R}$ related to the ring’s idempotent elements, nilpotent elements, zero divisor eleme...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Naim Çağman
2022-12-01
|
| Series: | Journal of New Theory |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/2710727 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849723716023353344 |
|---|---|
| author | Didem Karalarlıoğlu Camcı Didem Yeşil |
| author_facet | Didem Karalarlıoğlu Camcı Didem Yeşil |
| author_sort | Didem Karalarlıoğlu Camcı |
| collection | DOAJ |
| description | In this study, we define a new concept, i.e., source of primeness of a ring $R$, as $P_{R} := \bigcap_{a\in R} S_{R}^{a}$ such that $S_{R}^{a}:=\{b\in R \mid aRb=(0)\}$. We then examine some basic properties of $P_{R}$ related to the ring’s idempotent elements, nilpotent elements, zero divisor elements, and identity elements. Finally, we discuss the need for further research. |
| format | Article |
| id | doaj-art-5fa6bfc098c644a790fa69979b1e46a5 |
| institution | DOAJ |
| issn | 2149-1402 |
| language | English |
| publishDate | 2022-12-01 |
| publisher | Naim Çağman |
| record_format | Article |
| series | Journal of New Theory |
| spelling | doaj-art-5fa6bfc098c644a790fa69979b1e46a52025-08-20T03:10:57ZengNaim ÇağmanJournal of New Theory2149-14022022-12-014110010410.53570/jnt.11896512425The Source of Primeness of RingsDidem Karalarlıoğlu Camcı0https://orcid.org/0000-0002-8413-3753Didem Yeşil1https://orcid.org/0000-0003-0666-9410CANAKKALE ONSEKIZ MART UNIVERSITYÇANAKKALE ONSEKİZ MART ÜNİVERSİTESİIn this study, we define a new concept, i.e., source of primeness of a ring $R$, as $P_{R} := \bigcap_{a\in R} S_{R}^{a}$ such that $S_{R}^{a}:=\{b\in R \mid aRb=(0)\}$. We then examine some basic properties of $P_{R}$ related to the ring’s idempotent elements, nilpotent elements, zero divisor elements, and identity elements. Finally, we discuss the need for further research.https://dergipark.org.tr/en/download/article-file/2710727prime ringsemiprime ringsource of primenesssource of semiprimeness |
| spellingShingle | Didem Karalarlıoğlu Camcı Didem Yeşil The Source of Primeness of Rings Journal of New Theory prime ring semiprime ring source of primeness source of semiprimeness |
| title | The Source of Primeness of Rings |
| title_full | The Source of Primeness of Rings |
| title_fullStr | The Source of Primeness of Rings |
| title_full_unstemmed | The Source of Primeness of Rings |
| title_short | The Source of Primeness of Rings |
| title_sort | source of primeness of rings |
| topic | prime ring semiprime ring source of primeness source of semiprimeness |
| url | https://dergipark.org.tr/en/download/article-file/2710727 |
| work_keys_str_mv | AT didemkaralarlıoglucamcı thesourceofprimenessofrings AT didemyesil thesourceofprimenessofrings AT didemkaralarlıoglucamcı sourceofprimenessofrings AT didemyesil sourceofprimenessofrings |