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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Separable topological algebras. I


Author: Michael J. Liddell
Journal: Trans. Amer. Math. Soc. 195 (1974), 31-59
MSC: Primary 46H05; Secondary 46M20
MathSciNet review: 0352985
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Abstract: Let A be a complete topological algebra with identity and B a subalgebra of the center of A. A notion of relative topological tensor product $ {\hat \otimes _B}$ for topological A modules and the resultant relative homology theory are introduced. Algebras of bidimension zero in this sense are called separable relative to B. Structure theorems are proved for such algebras under various topological assumptions on the algebra and its maximal ideal space.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0352985-9
Keywords: Splitting idempotent, separability, homogeneity, matrix-modular algebras, l.m.c. algebras, nuclearity, fully complete spaces, WSD spaces, projective tensor product, relative topological tensor product, split exact sequence
Article copyright: © Copyright 1974 American Mathematical Society