On weakly 2-absorbing ideals of commutative rings
Let R be a commutative ring with identity 1 not equal to 0. In this paper, we introduce the concept of a weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing ideal of R if whenever abc is not equal to 0 for some a, b, c in R and abc is in I, then ab is in I or ac is in I or...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | article |
| Published: |
2013
|
| Online Access: | http://hdl.handle.net/11073/9226 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1864513438478237696 |
|---|---|
| author | Badawi, Ayman |
| author2 | Darani, Ahmad Yousefian |
| author2_role | author |
| author_facet | Badawi, Ayman Darani, Ahmad Yousefian |
| author_role | author |
| dc.creator.none.fl_str_mv | Badawi, Ayman Darani, Ahmad Yousefian |
| dc.date.none.fl_str_mv | 2013 2018-02-28T05:33:04Z 2018-02-28T05:33:04Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Badawi, A. (2013). On weakly 2-absorbing ideals of commutative rings. Houston journal of mathematics, 39(2), 441-452. 0362-1588 http://hdl.handle.net/11073/9226 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | University of Houston |
| dc.relation.none.fl_str_mv | http://www.math.uh.edu/~hjm/Vol39-2.html |
| dc.title.none.fl_str_mv | On weakly 2-absorbing ideals of commutative rings |
| dc.type.none.fl_str_mv | Published version Peer-Reviewed info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | Let R be a commutative ring with identity 1 not equal to 0. In this paper, we introduce the concept of a weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing ideal of R if whenever abc is not equal to 0 for some a, b, c in R and abc is in I, then ab is in I or ac is in I or bc is in I. For example, every proper ideal of a quasi-local ring (R,M) with M3 equals {0} is a weakly 2-absorbing ideal of R. We show that a weakly 2-absorbing ideal I of R with I3 not equal to {0} is a 2-absorbing ideal of R. We show that every proper ideal of a commutative ring R is a weakly 2-absorbing ideal if and only if either R is a quasi-local ring with maximal ideal M such that M3 equals {0} or R is ring-isomorphic to (R1 × F) where R1 is a quasi-local ring with maximal ideal M such that M2 equals {0} and F is a field or R is ring-isomorphic to (F1 × F2 × F3) for some fields F1, F2, F3. |
| format | article |
| id | aus_7702e7f7dbcd0718105eb1dcdacc36d2 |
| identifier_str_mv | Badawi, A. (2013). On weakly 2-absorbing ideals of commutative rings. Houston journal of mathematics, 39(2), 441-452. 0362-1588 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/9226 |
| publishDate | 2013 |
| publisher.none.fl_str_mv | University of Houston |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | On weakly 2-absorbing ideals of commutative ringsBadawi, AymanDarani, Ahmad YousefianLet R be a commutative ring with identity 1 not equal to 0. In this paper, we introduce the concept of a weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing ideal of R if whenever abc is not equal to 0 for some a, b, c in R and abc is in I, then ab is in I or ac is in I or bc is in I. For example, every proper ideal of a quasi-local ring (R,M) with M3 equals {0} is a weakly 2-absorbing ideal of R. We show that a weakly 2-absorbing ideal I of R with I3 not equal to {0} is a 2-absorbing ideal of R. We show that every proper ideal of a commutative ring R is a weakly 2-absorbing ideal if and only if either R is a quasi-local ring with maximal ideal M such that M3 equals {0} or R is ring-isomorphic to (R1 × F) where R1 is a quasi-local ring with maximal ideal M such that M2 equals {0} and F is a field or R is ring-isomorphic to (F1 × F2 × F3) for some fields F1, F2, F3.University of Houston2018-02-28T05:33:04Z2018-02-28T05:33:04Z2013Published versionPeer-Reviewedinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfBadawi, A. (2013). On weakly 2-absorbing ideals of commutative rings. Houston journal of mathematics, 39(2), 441-452.0362-1588http://hdl.handle.net/11073/9226en_UShttp://www.math.uh.edu/~hjm/Vol39-2.htmloai:repository.aus.edu:11073/92262024-08-22T12:02:07Z |
| spellingShingle | On weakly 2-absorbing ideals of commutative rings Badawi, Ayman |
| status_str | publishedVersion |
| title | On weakly 2-absorbing ideals of commutative rings |
| title_full | On weakly 2-absorbing ideals of commutative rings |
| title_fullStr | On weakly 2-absorbing ideals of commutative rings |
| title_full_unstemmed | On weakly 2-absorbing ideals of commutative rings |
| title_short | On weakly 2-absorbing ideals of commutative rings |
| title_sort | On weakly 2-absorbing ideals of commutative rings |
| url | http://hdl.handle.net/11073/9226 |