Turkish Journal of Mathematics




Some characterizations of strongly regular rings will be given. Let R be a ring and I(\neq R) a right ideal of R. If, for each pair of right ideals A and B of R, AB \subseteq I implies that either A \subseteq I or B \subseteq I, then I is called a prime right ideal (or equivalently, if aRb \ \ \not\subseteq I whenever a and b do not belong to I). I is strongly prime right ideal if, for each pair of a and b in R, aIb \subseteq I and ab \in I imply that either a \in I or b \in I, and we call I a strongly semiprime right ideal whenever a I a \subseteq I and a^2 \in I imply that a \in I. A strongly prime right ideal is trivially strongly semiprime, but the converse need not be true, as the following example shows:

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