What is it about?
It generalizes a well-known and a very useful result in commutative rings to non-commutative rings with a natural proof.
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Why is it important?
For a long time it was folklore that this result is a commutative result. After its study in non-commutative rings a useful related result in commutative rings is observed, which has been overlooked in all these years even in commutative rings and it also proves to have applications in number theory.
Perspectives
For a long time (at least for 3 decades) I have been proving the prime avoidance lemma in the classroom as it is proved in the article. I hope to see some non-commutative textbooks written in the future in which the Lemma is dealt with as in the article
Omid Ali Shahni Karamzadeh
Institute for Research in Fundamental Sciences
Read the Original
This page is a summary of: The Prime Avoidance Lemma Revisited, Kyungpook mathematical journal, June 2012, Department of Mathematics, Kyungpook National University,
DOI: 10.5666/kmj.2012.52.2.149.
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