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...

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التفاصيل البيبلوغرافية
المؤلف الرئيسي: Badawi, Ayman (author)
مؤلفون آخرون: Jaballah, Ali (author)
التنسيق: article
منشور في: 2008
الوصول للمادة أونلاين:http://hdl.handle.net/11073/9225
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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.
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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
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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