| 31. | These ideas can then be extended to the non-commutative case.
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| 32. | The equivariance condition can also be understood as the following commutative diagram.
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| 33. | This is the subject of non-commutative harmonic analysis.
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| 34. | Nest algebras are among the simplest examples of commutative subspace lattice algebras.
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| 35. | Vector spaces over a localization of a commutative ring are flat modules.
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| 36. | Flat modules over commutative rings are always torsion-free.
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| 37. | To simplify this discussion we shall assume that is a commutative operation.
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| 38. | Tannaka Krein duality is a non-commutative analogue of Pontryagin duality.
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| 39. | This technique works because addition is both associative and commutative.
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| 40. | More generally, every commutative topological group is also a uniform space.
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