Abstract
For a hereditary torsion theory τ, we show by examples that the concepts of τ-Artinian τ-simple, τ-Artinian τ-primitive, τ-Artinian τ-prime, τ-Artinian τ-semiprimitive, and τ-Artinian τ-semiprime rings are different from each other and thus answer a question raised by Bland in his book [Topics in Torsion Theory, (Mathematical Research, 103, Wiley-VCH, 1998]. The example of a τ-Artinian τ-primitive ring which is not τ-simple here appears to be a counter-example to a result of Bland in the same publication.
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