On some properties of polynomials rings
For a commutative ring with unity R, it is proved that R is a PF-ring if and only if the annihilator, annR(a), for each a ϵ R is a pure ideal in R, Also it is proved that the polynomial ring, R[X], is a PF-ring if and only if R is a PF-ring. Finally, we prove that R is a PP-ring if and only if R[X]...
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171287000371 |
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| _version_ | 1832549811191021568 |
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| author | H. Al-Ezeh |
| author_facet | H. Al-Ezeh |
| author_sort | H. Al-Ezeh |
| collection | DOAJ |
| description | For a commutative ring with unity R, it is proved that R is a PF-ring if and only if the annihilator, annR(a), for each a ϵ R is a pure ideal in R, Also it is proved that the polynomial ring, R[X], is a PF-ring if and only if R is a PF-ring. Finally, we prove that R is a PP-ring if and only if R[X] is a PP-ring. |
| format | Article |
| id | doaj-art-9e6c1219a189427eaa98755d13c6af1b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-9e6c1219a189427eaa98755d13c6af1b2025-02-03T06:08:31ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110231131410.1155/S0161171287000371On some properties of polynomials ringsH. Al-Ezeh0Department of Mathematics, University of Jordan, Amman, JordanFor a commutative ring with unity R, it is proved that R is a PF-ring if and only if the annihilator, annR(a), for each a ϵ R is a pure ideal in R, Also it is proved that the polynomial ring, R[X], is a PF-ring if and only if R is a PF-ring. Finally, we prove that R is a PP-ring if and only if R[X] is a PP-ring.http://dx.doi.org/10.1155/S0161171287000371polynomial ringspure idealPF-ringPP-ringR-flatnessand idempotent elements. |
| spellingShingle | H. Al-Ezeh On some properties of polynomials rings International Journal of Mathematics and Mathematical Sciences polynomial rings pure ideal PF-ring PP-ring R-flatness and idempotent elements. |
| title | On some properties of polynomials rings |
| title_full | On some properties of polynomials rings |
| title_fullStr | On some properties of polynomials rings |
| title_full_unstemmed | On some properties of polynomials rings |
| title_short | On some properties of polynomials rings |
| title_sort | on some properties of polynomials rings |
| topic | polynomial rings pure ideal PF-ring PP-ring R-flatness and idempotent elements. |
| url | http://dx.doi.org/10.1155/S0161171287000371 |
| work_keys_str_mv | AT halezeh onsomepropertiesofpolynomialsrings |