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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Submodules of $ C(X)\times \cdots \times C(X)$


Author: B. Roth
Journal: Proc. Amer. Math. Soc. 32 (1972), 543-548
MSC: Primary 46E15; Secondary 13C99
MathSciNet review: 0293382
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Abstract: Let $ C(X)$ be the ring of continuous real-valued functions on a compact Hausdorff space X with the sup norm topology. In the present paper, the closed submodules of the $ C(X)$-module $ C(X) \times \cdots \times C(X)$ are characterized and a necessary and sufficient condition for a submodule of $ C(X) \times \cdots \times C(X)$ to be closed and finitely generated is established.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0293382-8
Keywords: Rings of continuous functions, modules of continuous functions, submodules of continuous functions, finitely generated submodules
Article copyright: © Copyright 1972 American Mathematical Society