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Abstract
In [Citation2] Camillo and Zelmanowitz stated that rings all whose modules are dimension modules are semisimple Artinian. It seem however that the proof in [Citation2] 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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Notes
1An infinite cardinal κ is called regular if κ
i
< κ for i ∈ I with |I| < κ implies . An uncountable, regular, limit cardinal is said to be inaccessible. According to [Citation3, p. 297] “..the existence of inaccessible cardinals cannot be proved in ZFC [..] and in the constructible universe there are no such cardinals.”
Communicated by T. Albu.