Abstract
In order to have a self-contained discussion about universal coefficient theorems, coefficient groups and their effects on quantum field theories some supplemental concepts must be introduced. I suppose that the concept of ring is well understood. Basically it represents a set of elements for which we can define two operations: multiplication and addition. The set is then a group for addition and a monoid for multiplication while the multiplication is distributive with respect to addition. The set can contain not only numbers but various other objects. In the theory of rings we can define the so called ideal of a ring. For a ring \((R,+,\cdot )\) we consider \((R,+)\) to be its additive group. We call a subset I its ideal if it is an additive subgroup of R that absorbs through multiplication by elements of R all the other elements.
‘Do you know, I always thought unicorns were fabulous monsters, too? I never saw one alive before!’
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Lewis Carroll, Alice in Wonderland
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Patrascu, AT. (2017). From Grothendieck’s Schemes to QCD. In: The Universal Coefficient Theorem and Quantum Field Theory. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-46143-4_11
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