Some Basic Theorems
- The Isomorphism theorems, which encompass the isomorphism theorems of groups, rings, modules, etc.
- Birkhoff's HSP Theorem, which states that a class of algebras is a variety if and only if it is closed under homomorphic images, subalgebras, and arbitrary direct products.
Read more about this topic: Universal Algebra
Famous quotes containing the word basic:
“What, then, is the basic difference between today’s computer and an intelligent being? It is that the computer can be made to see but not to perceive. What matters here is not that the computer is without consciousness but that thus far it is incapable of the spontaneous grasp of pattern—a capacity essential to perception and intelligence.”
—Rudolf Arnheim (b. 1904)