Vol. 51, No. 1, 1974

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Intrinsic extensions of prime rings

K. C. O’Meara

Vol. 51 (1974), No. 1, 257–269

A ring extension S of a ring R is right intrinsic over R, in the sense of Faith and Utumi, if A R0 for each nonzero right ideal A of S. S is a right quotient ring of R, in the sense of R. E. Johnson, if SR is an essential extension of RR. Let 𝒞 be the class of prime rings which have zero right singular ideal and contain uniform right ideals. This paper deals with two questions:

  1. If S ∈𝒞 and S is right intrinsic over a prime ring R, is S a right quotient ring of R?
  2. If R ∈𝒞 and S is right intrinsic over R, is S a right quotient ring of R?

The main result is that the answer to (1) is “yes” provided S is not an integral domain. As a consequence of this, a partial answer to (2) is “yes” provided R is not an integral domain and R contains a nonzero finite dimensional right annihilator ideal.

Mathematical Subject Classification
Primary: 16A12
Received: 18 December 1972
Revised: 13 April 1973
Published: 1 March 1974
K. C. O’Meara