Note on Colon-Multiplication Domains
Let R be an integral domain with quotient field L. Call a nonzero (fractional) ideal A of R a colon-multiplication ideal any ideal A, such that B(A:B)=A for every nonzero (fractional) ideal B of R. In this note, we characterize integral domains for which every maximal ideal (resp., every nonzero i...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/231326 |
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| author | A. Mimouni |
| author_facet | A. Mimouni |
| author_sort | A. Mimouni |
| collection | DOAJ |
| description | Let R be an integral domain with quotient field L. Call a nonzero (fractional) ideal A of R a colon-multiplication ideal any ideal A, such that B(A:B)=A
for every nonzero (fractional) ideal B of R. In this note, we characterize integral domains for which every maximal ideal (resp., every nonzero ideal) is a colon-multiplication ideal. It turns that this notion unifies Dedekind and MTP domains. |
| format | Article |
| id | doaj-art-ccc844340d5c4b538cd31be4f30ef1a5 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ccc844340d5c4b538cd31be4f30ef1a52025-08-20T02:19:57ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/231326231326Note on Colon-Multiplication DomainsA. Mimouni0Department of Mathematics and Statistics, King Fahd University of Petroleum & Minerals, P.O. Box 278, Dhahran 31261, Saudi ArabiaLet R be an integral domain with quotient field L. Call a nonzero (fractional) ideal A of R a colon-multiplication ideal any ideal A, such that B(A:B)=A for every nonzero (fractional) ideal B of R. In this note, we characterize integral domains for which every maximal ideal (resp., every nonzero ideal) is a colon-multiplication ideal. It turns that this notion unifies Dedekind and MTP domains.http://dx.doi.org/10.1155/2010/231326 |
| spellingShingle | A. Mimouni Note on Colon-Multiplication Domains International Journal of Mathematics and Mathematical Sciences |
| title | Note on Colon-Multiplication Domains |
| title_full | Note on Colon-Multiplication Domains |
| title_fullStr | Note on Colon-Multiplication Domains |
| title_full_unstemmed | Note on Colon-Multiplication Domains |
| title_short | Note on Colon-Multiplication Domains |
| title_sort | note on colon multiplication domains |
| url | http://dx.doi.org/10.1155/2010/231326 |
| work_keys_str_mv | AT amimouni noteoncolonmultiplicationdomains |