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MÜLLER’S QUESTION ON SEMI-PERFECT COMPLETE HEREDITARY NOETHERIAN PRIME RINGS

Published online by Cambridge University Press:  25 January 2007

Pham Ngoc Ánh  and
Dolors Herbera
Pham Ngoc Ánh
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences, PO Box 127, 1364 Budapest, Hungary (anh@renyi.hu)
Dolors Herbera
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain (dolors@manwe.mat.uab.es)
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Abstract

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A positive answer to a question of Müller is given: any semi-perfect complete hereditary Noetherian prime ring $R$ has a weakly symmetric self-duality sending every ideal $I$ to its cycle-neighbour $X$. Consequently, the factor rings $R/I$ and $R/X$ are isomorphic without using the 1984 results of Dischinger and Müller.

Keywords

Primary 16D5016D9016E60Morita dualityNoetherian prime ringshereditaryinjective moduleslocalizationsquotient rings
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 3 , October 2006 , pp. 567 - 573
Copyright
Copyright © Edinburgh Mathematical Society 2006