Associated prime ideals of weak σ-rigid rings and their extensions
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Associated prime ideals of weak σ-rigid rings and their extensions
|
|
| Creator |
Bhat, V.K.
|
|
| Description |
Let R be a right Noetherian ring which is also an algebra over Q (Q the field of rational numbers). Let σ be an automorphism of R and δ a σ-derivation of R. Let further σ be such that aσ(a)∈N(R) implies that a∈N(R) for a∈R, where N(R) is the set of nilpotent elements of R. In this paper we study the associated prime ideals of Ore extension R[x;σ,δ] and we prove the following in this direction: Let R be a semiprime right Noetherian ring which is also an algebra over Q. Let σ and δ be as above. Then P is an associated prime ideal of R[x;σ,δ] (viewed as a right module over itself) if and only if there exists an associated prime ideal U of R with σ(U)=U and δ(U)⊆U and P=U[x;σ,δ]. We also prove that if R be a right Noetherian ring which is also an algebra over Q, σ and δ as usual such that σ(δ(a))=δ(σ(a)) for all a∈R and σ(U)=U for all associated prime ideals U of R (viewed as a right module over itself), then P is an associated prime ideal of R[x;σ,δ] (viewed as a right module over itself) if and only if there exists an associated prime ideal U of R such that (P∩R)[x;σ,δ]=P and P∩R=U. |
|
| Date |
2019-06-15T16:14:20Z
2019-06-15T16:14:20Z 2010 |
|
| Type |
Article
|
|
| Identifier |
Associated prime ideals of weak σ-rigid rings and their extensions / V.K. Bhat // Algebra and Discrete Mathematics. — 2010. — Vol. 10, № 1. — С. 8–17. — Бібліогр.: 15 назв. — англ.
1726-3255 2000 Mathematics Subject Classification:16-XX; 16N40, 16P40, 16S36. http://dspace.nbuv.gov.ua/handle/123456789/154506 |
|
| Language |
en
|
|
| Relation |
Algebra and Discrete Mathematics
|
|
| Publisher |
Інститут прикладної математики і механіки НАН України
|
|