| Langlands proposed a way of dealing with the more general, noncommutative case. |
| That new study on noncommutative symmetries looks promising. |
| 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. |
| However, algebraic notions and tools can be successfully utilized also in the noncommutative case. |
| Quaternion multiplication and matrix multiplication is also noncommutative. |
| Chapters address group theory, commutative rings, Galois theory, noncommutative rings, representation theory, advanced linear algebra, and homology. |
