| 41. | A topological group is a mathematical object with both an algebraic structure and a topological structure.
|
| 42. | This proof does not work for non-algebraic structures.
|
| 43. | Important other algebraic structures such as rings arise when requiring only part of the above axioms.
|
| 44. | The idea of describing algebraic structures with finite-automata can be generalized from groups to other structures.
|
| 45. | A forgetful functor between categories of algebraic structures " forgets " a part of a structure.
|
| 46. | A surjective homomorphism is always right cancelable, but the converse is not always true for algebraic structures.
|
| 47. | Formal definition through primitive operations and axioms were proposed for many basic algebraic structures, such as fields.
|
| 48. | But over the years he became known for his work in applying algebraic structures to real-life situations.
|
| 49. | Early results include ordered algebraic structures.
|
| 50. | Suppose A is an algebraic structure.
|
