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UBC Theses and Dissertations
Sub-rings of C(Rⁿ) Gan, Cheong Kuoon
Abstract
The content of this thesis contains a study of the rings C(Rⁿ), L[sub c](Rⁿ), C[sup m](Rⁿ), C[sup ∞](Rⁿ), А(Rⁿ) and P(Rⁿ). We obtain the result that no two of the rings above can be isomorphic : in fact we prove the following : if Φ : A → B is a ring homomorphism where A, B are any two of the rings and A ⊂ B, then Φ(f) = f(p) for some p εRⁿ. We also characterise C(Rⁿ), C[sup m](Rⁿ), and C[sup ∞](Rⁿ) as rings.
Item Metadata
| Title |
Sub-rings of C(Rⁿ)
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
1974
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| Description |
The content of this thesis contains a study of the rings C(Rⁿ), L[sub c](Rⁿ), C[sup m](Rⁿ), C[sup ∞](Rⁿ), А(Rⁿ) and P(Rⁿ). We obtain the result that no two of the rings above can be isomorphic : in fact we prove the following : if Φ : A → B is a ring homomorphism where A, B are any two of the rings and A ⊂ B, then Φ(f) = f(p) for some p εRⁿ. We also characterise C(Rⁿ), C[sup m](Rⁿ), and C[sup ∞](Rⁿ) as rings.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2010-01-29
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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| DOI |
10.14288/1.0080129
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Campus | |
| Scholarly Level |
Graduate
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| Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.