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Details van artikel 5 van 9 gevonden artikelen
| Titel: |
On nonsingular right fpf rings |
| Auteur: |
Buigess, W.D. |
| Verschenen in: |
Communications in algebra |
| Paginering: | Jaargang 12 (1984) nr. 14 pagina's 1729-1750 |
| Jaar: |
1984 |
| Inhoud: |
A right FPF ring is one over which every finitely generated faithful right module is a generator. The main purpose of the article is to givp the following cnaracterization of certain right FPF rings. TheoremLet R be semiprime and right semihereditary. Then R is right FPF iff (1) the right maximal ring of quotients Qr (R) = Q coincides with the left and right classical rings of quotients and is self-injective regular of bounded index, (ii) R and Q have the same central idem-potents, (iii) if I is an ideal of R generated by a maximal ideal of the boolean algebra of central idempotent s5 R/I is such that each non-zero finitely generated right ideal is a generator (hence prime), and (iv) R is such that every essential right ideal contains an ideal which is essential as a right ideal In case that R is semiprime and module finite over its centre C, then the above can be used to show that R is FPF (both sides) if and only if it is a semi-hereditary maximal C-order in a self-injective regular ring (of finite index) In order to prove the above it is shown that for any semiprime right FPF ring R, Qlcl(R) exists and coincides with Qr(R) (Faith and Page have shown that the latter is self-injective regular of bounded index). It R is semiprime right FPF and satisfies a polynamical identity then the factor rings as in (iii) above are right FPF and R is the ring of sections of a sheaf of prime right FPF rings The Proofs use many results of C. Faith and S Page as well as some of the techniques of Pierce sheaves |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 5 van 9 gevonden artikelen
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