Abstract
A ring which is an essential extension of a prime ring without proper prime homomorphic imges is called a *k-ring. *k-rings are characterized and it is shown that every non-zero prime ring whose every proper homomorphic image is artinian on right (left, two-sided) ideals can be homomorpically mapped onto a nonzero *k-ring. This gives a partial answer to Gardner's question (Problem 1 in [4]).
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