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Regular Rings are Very Regular
Canadian Mathematical Bulletin, 1982The following problem arose in a conversation with Abraham Zaks: “Suppose R is an associative ring with identity such that every finitely generated left ideal is generated by idempotents. Is R von-Neumann regular?” In the literature the “s” in “idempotents” is missing, and is replaced by “an idempotent”. The answer is, “Yes!”
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Geometric Regularity on Regular Manifolds
2021In this talk we discuss an approach to formalize the notion of "regularity", focusing specially on "regularity structures" on $C^k$-manifolds and on geometric objects, such as tensors,partial differential operators, connections on bundles,etc. We present an strategy that could be used to attack existence and multiplicity problems for these regularity ...
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