Classical Quotient Rings and Ordinary Extensions of 2-Primal Rings
| Autor: | Nam Kyun Kim, Mi Hyang Kwon, Yong Uk Cho, Yang Lee |
|---|---|
| Rok vydání: | 2006 |
| Předmět: | |
| Zdroj: | Algebra Colloquium. 13:513-523 |
| ISSN: | 0219-1733 1005-3867 |
| Popis: | We study classical right quotient rings and ordinary extensions of various kinds of 2-primal rings, constructing examples for situations that raise naturally in the process. We show: (1) Let R be a right Ore ring with P(R) left T-nilpotent. Then Q is a 2-primal local ring with P(Q)=J(Q) = {ab-1 ∈ Q | a ∈ P(R), b ∈ C(0)} if and only if C(0)=C(P(R))=R∖P(R), where Q is the classical right quotient ring of R. (2) Let R be a right Ore ring. Then R[x] is a domain whose classical right quotient ring is a division ring if and only if R is a right p.p. ring with C(P(R))=R∖P(R). As a consequence, if R is a right Noetherian ring, then R[[x]] is a domain whose classical right quotient ring is a division ring if and only if R[x] is a domain whose classical right quotient ring is a division ring if and only if R is a right p.p. ring with C(P(R))=R∖P(R). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|