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On simple, primitive and prime rings relative to a torsion theory

Published online by Cambridge University Press:  17 April 2009

John Dauns  and
Yiqiang Zhou
John Dauns
Affiliation:
Tulane University, New Orleans LA 70118–5698, United States of America
Yiqiang Zhou
Affiliation:
Memorial University of Newfoundland, St. John's NF A1C 5S7, Canada
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Abstract

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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 297 - 301
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Bland, P.E., Topics in torsion theory, Mathematical Research 103 Wiley-VCH Verlag, Berlin, 1998).Google Scholar
[2]Page, S.S. and Zhou, Y., ‘On direct sums of injective modules and chain conditions’ Canad. J. Math. 46 (1994), 634–647.CrossRefGoogle Scholar