. A C ] 2 6 A pr 2 00 4 THE DISCRETE GELFAND TRANSFORM AND ITS DUAL
نویسندگان
چکیده
We consider the transformation ev which associates to any element in a K-algebra A a function on the the set of its K-points. This is the analogue of the fundamental Gelfand transform. Both ev and its dual ev * are the maps from a discrete K-module to a topological K-module and we investigate in which case the image of each map is dense. The answer is nontrivial for various choices of K and A already for A=K[x], the polynomial ring in one variable. Applications to the structure of algebras of cohomology operations are given.
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The Gelfand Transform in Commutative Algebra
We consider the transformation ev which associates to any element in a K-algebra A a function on the the set of its K-points. This is the analogue of the fundamental Gelfand transform. Both ev and its dual ev∗ are the maps from a discrete K-module to a topological Kmodule and we investigate in which case the image of each map is dense. This question arises in the classical problem of the recons...
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