Abstract
It is proved that ifRis a semiprime ELT-ring and every simple rightR-module is flat thenRis regular. IsRregular ifRis a semiprime ELT-ring and every simple rightR-module is flat? In this note, we give a positive answer to the question.
Highlights
In [1] Yue Chi Ming proposed the following question: Is R regular if R is a semiprime ELT-ring and every simple right R-module is flat? In this note, we give a positive answer to the question
We begin by stating following lemmas which will be used in proof of our main result
LEMMA 2. ([5], Corollary 8.5) If R is a semiprime ring, .every minimal left ideal is generated by an idempotent
Summary
In [1] Yue Chi Ming proposed the following question: Is R regular if R is a semiprime ELT-ring and every simple right R-module is flat? In this note, we give a positive answer to the question. [1] Yue Chi Ming proposed the following question: Is R regular if R is a semiprime ELT- Ring and every simple right R-module is flat? We give a positive answer to the question. All rings considered in this paper are associative with identity, and all modules are unital.
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