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Perspectives on Amenability and Congeniality of Bases

Stanley, Benjamin Q.
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1551065156755937

Abstract Details

2019, Doctor of Philosophy (PhD), Ohio University, Mathematics (Arts and Sciences).
We provide topological interpretations of amenability and congeniality of bases of an infinite dimensional algebra A; in fact, we also extend these notions to bases over infinite dimensional A-modules. A basis B over an A-module T is called amenable if F^B, the direct product indexed by B of copies of the field 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. Not all bases that fail to be amenable do so the same way, we introduce means to measure how amenable a basis is. For a basis B this measure, its domain of amenability, turns out to be a subalgebra of A. The collection of all such domains of amenability of bases is called the profile of T . We explore possible profiles of modules and show an example of a module that has as small a profile as possible. We extend the recently obtained result that there exist magma algebras that have neither simple nor projective bases to show that, in fact, no magma algebra has any projective bases.
Sergio Lopez-Permouth (Advisor)
Vladimir Uspenskiy (Committee Member)
Davydov Alexei (Committee Member)
Jeffrey Dill (Committee Member)
95 p.
Mathematics
Amenable bases; Congeniality of bases; Schauder bases; Infinite-dimensional modules; algebras; Basic Modules; Contrarian Bases; Amenability Profiles; Domain of Amenability

Recommended Citations

Citations

  • Stanley, B. Q. (2019). Perspectives on Amenability and Congeniality of Bases [Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1551065156755937

    APA Style (7th edition)

  • Stanley, Benjamin. Perspectives on Amenability and Congeniality of Bases. 2019. Ohio University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1551065156755937.

    MLA Style (8th edition)

  • Stanley, Benjamin. "Perspectives on Amenability and Congeniality of Bases." Doctoral dissertation, Ohio University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1551065156755937

    Chicago Manual of Style (17th edition)

ohiou1551065156755937
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© 2019, all rights reserved.
This open access ETD is published by Ohio University and OhioLINK.