The tensor product of topological modules over a ring
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Abstract
Tensor products provide an essential tool in the theory of rings and modules, but its topological structure has been rarely studied. In the present article, we give a foundational description of a natural topology on the (algebraic) tensor product of topological modules over a commutative topological ring. Our approach is to give a topology directly to the algebraic tensor product instead of introducing an universal object in the category of topological modules with respect to continuous bilinear maps.
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