Vol. 35, No. 3, 1970

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Rings whose homomorphic images are q-rings

Saad H. Mohamed

Vol. 35 (1970), No. 3, 727–735

L. Levy has characterised a commutative noetherian ring in which every proper homomorphic image is self-injective to be a Dedekind domain, or a principal ideal ring with descending chain condition, or a local ring whose maximal ideal M has composition length 2 and satisfies M2 = 0. The object of this paper is to generalise Levy’s result to the noncommutative case by studying right noetherian rings in which every proper homomorphic image is a right q-ring. Since every commutative self-injective ring is a q-ring, one can get Levy’s result as a special case of Theorems 2.12 and 2.13.

Mathematical Subject Classification
Primary: 16.25
Received: 15 April 1969
Published: 1 December 1970
Saad H. Mohamed