The Künneth theorem computes the homology or cohomology of a product from those of its factors. Over a field , as graded rings under suitable finiteness hypotheses.
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The Künneth theorem is an important result in algebraic topology that relates the homology groups of a product of two topological spaces to the homology groups of the individual spaces. It is particularly useful in the computation of homology groups for spaces that can be expressed as products of simpler spaces.