The Armendariz module and its application to the Ikeda-Nakayama module
A ring R is called a right Ikeda-Nakayama (for short IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the left annihilators, that is, if ℓ(I∩J)=ℓ(I)+ℓ(J) for all right ideals I and J of R. R is called Armendariz ring if whenever polynomials f(x)=a0+a1x+⋯+am...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS/2006/35238 |
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| author | M. Tamer Koşan |
| author_facet | M. Tamer Koşan |
| author_sort | M. Tamer Koşan |
| collection | DOAJ |
| description | A ring R is called a right Ikeda-Nakayama
(for short IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the left annihilators, that is, if ℓ(I∩J)=ℓ(I)+ℓ(J) for all right ideals I and J of R. R is called Armendariz ring if whenever polynomials f(x)=a0+a1x+⋯+amxm, g(x)=b0+b1x+⋯+bnxn∈R[x] satisfy f(x)g(x)=0, then aibj=0 for each i,j. In this paper, we show that if R[x] is a right IN-ring, then R is a right IN-ring in case R is an Armendariz ring. |
| format | Article |
| id | doaj-art-e372ab6dba274676b770c95981f01a68 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e372ab6dba274676b770c95981f01a682025-02-03T06:00:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252006-01-01200610.1155/IJMMS/2006/3523835238The Armendariz module and its application to the Ikeda-Nakayama moduleM. Tamer Koşan0Department of Mathematic, Faculty of Science-Literature, Kocatepe University, ANS Campus, Afyon 03200, TurkeyA ring R is called a right Ikeda-Nakayama (for short IN-ring) if the left annihilator of the intersection of any two right ideals is the sum of the left annihilators, that is, if ℓ(I∩J)=ℓ(I)+ℓ(J) for all right ideals I and J of R. R is called Armendariz ring if whenever polynomials f(x)=a0+a1x+⋯+amxm, g(x)=b0+b1x+⋯+bnxn∈R[x] satisfy f(x)g(x)=0, then aibj=0 for each i,j. In this paper, we show that if R[x] is a right IN-ring, then R is a right IN-ring in case R is an Armendariz ring.http://dx.doi.org/10.1155/IJMMS/2006/35238 |
| spellingShingle | M. Tamer Koşan The Armendariz module and its application to the Ikeda-Nakayama module International Journal of Mathematics and Mathematical Sciences |
| title | The Armendariz module and its application to the Ikeda-Nakayama
module |
| title_full | The Armendariz module and its application to the Ikeda-Nakayama
module |
| title_fullStr | The Armendariz module and its application to the Ikeda-Nakayama
module |
| title_full_unstemmed | The Armendariz module and its application to the Ikeda-Nakayama
module |
| title_short | The Armendariz module and its application to the Ikeda-Nakayama
module |
| title_sort | armendariz module and its application to the ikeda nakayama module |
| url | http://dx.doi.org/10.1155/IJMMS/2006/35238 |
| work_keys_str_mv | AT mtamerkosan thearmendarizmoduleanditsapplicationtotheikedanakayamamodule AT mtamerkosan armendarizmoduleanditsapplicationtotheikedanakayamamodule |