A Note on Dimension Modules |
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| Authors: | Christian Lomp Edmund Puczyłowski |
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| Affiliation: | 1. Department of Mathematics of the Faculty of Science and Center of Mathematics , University of Porto , Porto , Portugal clomp@fc.up.pt;3. Institute of Mathematics , University of Warsaw , Warsaw , Poland |
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| Abstract: | In [2 Camillo , V. P. , Zelmanowitz , J. M. ( 1980 ). Dimension modules . Pacific J. Math. 91 : 249 – 261 .[Crossref], [Web of Science ®] , [Google Scholar]] Camillo and Zelmanowitz stated that rings all whose modules are dimension modules are semisimple Artinian. It seem however that the proof in [2 Camillo , V. P. , Zelmanowitz , J. M. ( 1980 ). Dimension modules . Pacific J. Math. 91 : 249 – 261 .[Crossref], [Web of Science ®] , [Google Scholar]] contains a gap and applies to rings with finite Goldie dimension only. In this paper we show that the result indeed holds for all rings with a basis as well as for all commutative rings with Goldie dimension attained. |
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| Keywords: | Dimension formula Infinite Goldie dimension |
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