Some finiteness conditions on the set of overrings of a phi-ring
Let H = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. For a ring R in H with total quotient ring T(R), Let phi be the natural ring homomorphism from T(R) into R_Nil(R). An integral domain R is said to be an FC-domain (in the sense of Gilmer) if each chain of distinct overri...
محفوظ في:
| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | |
| التنسيق: | article |
| منشور في: |
2008
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| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/9225 |
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| _version_ | 1864513434859601920 |
|---|---|
| author | Badawi, Ayman |
| author2 | Jaballah, Ali |
| author2_role | author |
| author_facet | Badawi, Ayman Jaballah, Ali |
| author_role | author |
| dc.creator.none.fl_str_mv | Badawi, Ayman Jaballah, Ali |
| dc.date.none.fl_str_mv | 2008 2018-02-28T05:20:10Z 2018-02-28T05:20:10Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Badawi, A. (2008). Some finiteness conditions on the set of overrings of a phi-ring. Houston journal of mathematics, 34(2), 397-408. 0362-1588 http://hdl.handle.net/11073/9225 |
| 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/Vol34-2.html |
| dc.title.none.fl_str_mv | Some finiteness conditions on the set of overrings of a phi-ring |
| dc.type.none.fl_str_mv | Published version Peer-Reviewed info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | Let H = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. For a ring R in H with total quotient ring T(R), Let phi be the natural ring homomorphism from T(R) into R_Nil(R). An integral domain R is said to be an FC-domain (in the sense of Gilmer) if each chain of distinct overrings of R is finite, and R is called an FO-domain if R has finitely many overrings. A ring R is called an FC-ring if each chain of distinct overrings of R is finite, and R is said to be an FO-ring if R has finitely many overrings. A ring R in H is said to be a phi-FC-ring if phi(R) is an FC-ring, and R is called a phi-FO-ring if phi(R) is an FO-ring. In this paper, we show that the theory of phi-FC-rings and phi-FO-rings resembles that of FC-domains and FO-domains. |
| format | article |
| id | aus_c14d00c5a81446655ed09e2c83e99438 |
| identifier_str_mv | Badawi, A. (2008). Some finiteness conditions on the set of overrings of a phi-ring. Houston journal of mathematics, 34(2), 397-408. 0362-1588 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/9225 |
| publishDate | 2008 |
| publisher.none.fl_str_mv | University of Houston |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | Some finiteness conditions on the set of overrings of a phi-ringBadawi, AymanJaballah, AliLet H = {R | R is a commutative ring and Nil(R) is a divided prime ideal of R}. For a ring R in H with total quotient ring T(R), Let phi be the natural ring homomorphism from T(R) into R_Nil(R). An integral domain R is said to be an FC-domain (in the sense of Gilmer) if each chain of distinct overrings of R is finite, and R is called an FO-domain if R has finitely many overrings. A ring R is called an FC-ring if each chain of distinct overrings of R is finite, and R is said to be an FO-ring if R has finitely many overrings. A ring R in H is said to be a phi-FC-ring if phi(R) is an FC-ring, and R is called a phi-FO-ring if phi(R) is an FO-ring. In this paper, we show that the theory of phi-FC-rings and phi-FO-rings resembles that of FC-domains and FO-domains.University of Houston2018-02-28T05:20:10Z2018-02-28T05:20:10Z2008Published versionPeer-Reviewedinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfBadawi, A. (2008). Some finiteness conditions on the set of overrings of a phi-ring. Houston journal of mathematics, 34(2), 397-408.0362-1588http://hdl.handle.net/11073/9225en_UShttp://www.math.uh.edu/~hjm/Vol34-2.htmloai:repository.aus.edu:11073/92252024-08-22T12:02:12Z |
| spellingShingle | Some finiteness conditions on the set of overrings of a phi-ring Badawi, Ayman |
| status_str | publishedVersion |
| title | Some finiteness conditions on the set of overrings of a phi-ring |
| title_full | Some finiteness conditions on the set of overrings of a phi-ring |
| title_fullStr | Some finiteness conditions on the set of overrings of a phi-ring |
| title_full_unstemmed | Some finiteness conditions on the set of overrings of a phi-ring |
| title_short | Some finiteness conditions on the set of overrings of a phi-ring |
| title_sort | Some finiteness conditions on the set of overrings of a phi-ring |
| url | http://hdl.handle.net/11073/9225 |