Topological characterizations of amenability and congeniality of bases
A basis B over an innite dimensional F-algebra A is called amenable if FB, the direct product indexed by B of copies of the eld F, can be made into an A-module in a natural way. (Mutual) congeniality is a relation that serves to identify cases when different amenable bases yield isomorphic A-modules.
(Not necessarily mutual) congeniality between amenable bases yields an epimorphism of the modules they induce. We prove that this epimorphism is one-to-one only if the congeniality is mutual, thus establishing a precise distinction between the two notions.
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1. On the amenability profile of infinite dimensional algebras
Sergio R. López-Permouth, Benjamin Stanley
Communications in Algebra first page: 1 year: 2021
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Universitat Politècnica de València
e-ISSN: 1989-4147 https://doi.org/10.4995/agt