On phi-Dedekind rings and phi-Krull rings
The purpose of this paper is to introduce two new classes of rings that are closely related to the classes of Dedekind domains and Krull domains. Let H = {R | R is a commutative ring with 1 and Nil(R) is a divided prime ideal of R}. Let R in H, T(R) be the total quotient ring of R, and let phi be th...
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| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | |
| التنسيق: | article |
| منشور في: |
2005
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| الوصول للمادة أونلاين: | http://hdl.handle.net/11073/9222 |
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| _version_ | 1864513442033958912 |
|---|---|
| author | Badawi, Ayman |
| author2 | Anderson, David F. |
| author2_role | author |
| author_facet | Badawi, Ayman Anderson, David F. |
| author_role | author |
| dc.creator.none.fl_str_mv | Badawi, Ayman Anderson, David F. |
| dc.date.none.fl_str_mv | 2005 2018-02-28T04:36:55Z 2018-02-28T04:36:55Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Anderson, D. F., & Badawi, A. (2005). On phi-Dedekind rings and phi-Krull rings. Houston journal of mathematics, 31(4), 1007-1022. 0362-1588 http://hdl.handle.net/11073/9222 |
| 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/Vol31-4.html |
| dc.title.none.fl_str_mv | On phi-Dedekind rings and phi-Krull rings |
| dc.type.none.fl_str_mv | Published version Peer-Reviewed info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | The purpose of this paper is to introduce two new classes of rings that are closely related to the classes of Dedekind domains and Krull domains. Let H = {R | R is a commutative ring with 1 and Nil(R) is a divided prime ideal of R}. Let R in H, T(R) be the total quotient ring of R, and let phi be the map from R into RNil(R) (the localization of R at Nil(R)) such that phi(a/b) = a/b for every a in R and b in R\ Z(R). Then phi is a ring homomorphism from T(R) into RNil(R), and phi restricted to R is also a ring homomorphism from R into RNil(R) given by phi(x) = x /1 for every x in R. A nonnil ideal I of R is said to be phi-invertible if phi(I) is an invertible ideal of phi(R). If every nonnil ideal of R is phi-invertible, then we say that R is a phi-Dedekind ring. Also, we say that R is a phi-Krull ring if phi(R) is the intersection of {Vi}, where each Vi is a discrete phi-chained overring of phi(R), and for every nonnilpotent element x in R , phi(x) is a unit in all but finitely many Vi. We show that the theories of phi-Dedekind and phi-Krull rings resemble those of Dedekind and Krull domains. |
| format | article |
| id | aus_4553620c221d076003de5483bbd4f473 |
| identifier_str_mv | Anderson, D. F., & Badawi, A. (2005). On phi-Dedekind rings and phi-Krull rings. Houston journal of mathematics, 31(4), 1007-1022. 0362-1588 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/9222 |
| publishDate | 2005 |
| publisher.none.fl_str_mv | University of Houston |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | On phi-Dedekind rings and phi-Krull ringsBadawi, AymanAnderson, David F.The purpose of this paper is to introduce two new classes of rings that are closely related to the classes of Dedekind domains and Krull domains. Let H = {R | R is a commutative ring with 1 and Nil(R) is a divided prime ideal of R}. Let R in H, T(R) be the total quotient ring of R, and let phi be the map from R into RNil(R) (the localization of R at Nil(R)) such that phi(a/b) = a/b for every a in R and b in R\ Z(R). Then phi is a ring homomorphism from T(R) into RNil(R), and phi restricted to R is also a ring homomorphism from R into RNil(R) given by phi(x) = x /1 for every x in R. A nonnil ideal I of R is said to be phi-invertible if phi(I) is an invertible ideal of phi(R). If every nonnil ideal of R is phi-invertible, then we say that R is a phi-Dedekind ring. Also, we say that R is a phi-Krull ring if phi(R) is the intersection of {Vi}, where each Vi is a discrete phi-chained overring of phi(R), and for every nonnilpotent element x in R , phi(x) is a unit in all but finitely many Vi. We show that the theories of phi-Dedekind and phi-Krull rings resemble those of Dedekind and Krull domains.University of Houston2018-02-28T04:36:55Z2018-02-28T04:36:55Z2005Published versionPeer-Reviewedinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfAnderson, D. F., & Badawi, A. (2005). On phi-Dedekind rings and phi-Krull rings. Houston journal of mathematics, 31(4), 1007-1022.0362-1588http://hdl.handle.net/11073/9222en_UShttp://www.math.uh.edu/~hjm/Vol31-4.htmloai:repository.aus.edu:11073/92222024-08-22T12:01:52Z |
| spellingShingle | On phi-Dedekind rings and phi-Krull rings Badawi, Ayman |
| status_str | publishedVersion |
| title | On phi-Dedekind rings and phi-Krull rings |
| title_full | On phi-Dedekind rings and phi-Krull rings |
| title_fullStr | On phi-Dedekind rings and phi-Krull rings |
| title_full_unstemmed | On phi-Dedekind rings and phi-Krull rings |
| title_short | On phi-Dedekind rings and phi-Krull rings |
| title_sort | On phi-Dedekind rings and phi-Krull rings |
| url | http://hdl.handle.net/11073/9222 |