Loading...
Please wait, while we are loading the content...
Similar Documents
Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bhat, Vijay K. |
| Copyright Year | 2013 |
| Abstract | AbstractLet R be a ring. We recall that R is called a near pseudo-valuation ring if every minimal prime ideal of R is strongly prime.Let now σ be an automorphism of R and δ a σ-derivation of R. Then R is said to be an almost δ-divided ring if every minimal prime ideal of R is δ-divided.Let R be a Noetherian ring which is also an algebra over ℚ (ℚ is the field of rational numbers). Let σ be an automorphism of R such that R is a σ(*)-ring and δ a σ-derivation of R such that σ(δ(a)) = δ(σ(a)) for all a ∈ R. Further, if for any strongly prime ideal U of R with σ(U) = U and δ(U) ⊆ δ, U[x; σ, δ] is a strongly prime ideal of R[x; σ, δ], then we prove the following: (1)R is a near pseudo valuation ring if and only if the Ore extension R[x; σ, δ] is a near pseudo valuation ring.(2)R is an almost δ-divided ring if and only if R[x; σ, δ] is an almost δ-divided ring. |
| Starting Page | 1049 |
| Ending Page | 1056 |
| Page Count | 8 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s10587-013-0071-8 |
| Alternate Webpage(s) | https://dml.cz/bitstream/handle/10338.dmlcz/143616/CzechMathJ_63-2013-4_14.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s10587-013-0071-8 |
| Volume Number | 63 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
