Abstract
We define a topology τe, on anyC-algebra of discrete valuation, generalizing the topology of coefficientwise convergence on C[[X]] studied by G. R. Allan. We give a necessary and sufficient condition for τe to be complete and prove that the completion provides an algebra of discrete valuation. We also prove that if aC-algebra of discrete valuation is Fréchet andm-convex for τe then it is isomorphic to (C[[X]], τe) and then τe is the uniqueF-algebra topology in A. We prove that a commutative, unital Fréchet l.m.c.a. that is aC-algebra of valuation is in fact aC-algebra of discrete valuation and so is embeddable in (C[[X]], τe). Whence a result of H. Bouloussa.
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Khlass, A.L., Oudadess, M. Structure des algebres de valuation discrete. Rend. Circ. Mat. Palermo 46, 439–450 (1997). https://doi.org/10.1007/BF02844283
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DOI: https://doi.org/10.1007/BF02844283