|
|||||
|
|
|
|
|
|
|
|
|
On regular
self-injective rings
Vasily Cateforis |
|
Vol. 30 (1969), No. 1, 39–45
|
Abstract |
|
If R is a right non-singular ring (with 1) and Q is its (R. E. Johnson) maximal right quotient ring, then the R-epimorphism ∑ ipi ⊗ qi →∑ piqi from (Q ⊗RQ)R to QR is not in general a monomorphism; in this paper we show that it is if, and only if, for each q ∈ Q,(R : q) = {r ∈ R|qr ∈ R} contains a finitely generated large right ideal of R. As a corollary to this we obtain: a (Von Neumann) regular ring R is right selfinjective if and only if every finitely generated nonsingular right R-module is projective. |
Mathematical Subject Classification
Primary: 16.90
|
Milestones
Received: 24 April 1968
Published: 1 July 1969
|
Authors |
| Vasily Cateforis | |
|
