Patrick F. Smith
Abstract
The main result of this paper states that if $R$ is a right Noetherian right bounded prime ring such that nonzero prime ideals are maximal and such that every proper homomorphic image of $R$ is a principal right ideal ring then $R$ is right hereditary.
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The main result of this paper states that if $R$ is a right Noetherian right bounded prime ring such that nonzero prime ideals are maximal and such that every proper homomorphic image of $R$ is a principal right ideal ring then $R$ is right hereditary.
Key concepts: Ideal (ethics), Mathematics, Principal ideal ring, Radical of a ring, Prime (order theory), Associated prime, Image (mathematics), Ring (chemistry)