• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.275-286
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• 2010

The algebraic structure of the natural integral cohomology operations is explored by means of examples. We decompose the generators of the groups $H^m(\mathbb{Z},\;n)$ with $2\;{\leq}\;n\;{\leq}\;7$ and $2\;{\leq}\;m\;{\leq}\;13$ into the operations of cup products, cross-cap products and compositions. Examination of these decompositions and comparison with other possible generators demonstrates the existence of relations between integral operations that have withheld formulation. The calculated groups and generators are collected in a table for practical reference.