| Langlands proposed a way of dealing with the more general, noncommutative case. |
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| This paper is devoted to the study of several interpretations of the algebra of noncommutative symmetric functions. |
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| Quaternion multiplication and matrix multiplication is also noncommutative. |
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| In 1843 the Irish mathematician-astronomer William Rowan Hamilton represented four-dimensional vectors algebraically and invented the quaternions, the first noncommutative algebra to be extensively studied. |
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| However, algebraic notions and tools can be successfully utilized also in the noncommutative case. |
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| This paper is devoted to the construction of several structures of acyclic complexes related with the algebra of noncommutative symmetric functions. |
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| Chapters address group theory, commutative rings, Galois theory, noncommutative rings, representation theory, advanced linear algebra, and homology. |
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| That new study on noncommutative symmetries looks promising. |
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| Michael Heller's is about noncommutative geometry as a recent example of why theories, whether mathematical or physical, of a self-contained universe never satisfy. |
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| Noncommutative analogues of classical operations on symmetric functions are investigated, and applied to the description of idempotents and nilpotents in descent algebras. |
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