Name
Abstract | ||
|---|---|---|
We continue the study of nil-Armendariz rings, initiated by Antoine, and Armendariz rings. We first examine a kind of ring coproduct constructed by Antoine for which the Armendariz, nil-Armendariz, and weak Armendariz properties are equivalent. Such a ring has an important role in the study of Armendariz ring property and near-related ring properties. We next prove an Antoine's result in relation with the ring coproduct by means of a simpler direct method. In the proof we can observe the concrete shapes of coefficients of zero-dividing polynomials. We next observe the structure of nil-Armendariz rings via the upper nilradicals. It is also shown that a ring R is Armendariz if and only if R is nil-Armendariz if and only if R is weak Armendariz, when R is a von Neumann regular ring. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1142/S0218196712500592 | INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION |
Keywords | Field | DocType |
Nil-Armendariz ring, Armendariz ring, polynomial ring, nilpotent element, nilradical, von Neumann regular ring | Reduced ring,Discrete mathematics,Boolean ring,Algebra,Primitive ring,Polynomial ring,Noncommutative ring,Ring (mathematics),Von Neumann regular ring,Mathematics,Principal ideal ring | Journal |
Volume | Issue | ISSN |
22 | 6 | 0218-1967 |
Citations | PageRank | References |
1 | 0.43 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Da Woon Jung | 1 | 14 | 3.54 |
| Nam-kyun Kim | 2 | 2 | 3.28 |
| Yang Lee | 3 | 4 | 3.28 |
| Sung Pil Yang | 4 | 1 | 0.43 |