Universal algebra (sometimes called general algebra) is the field of mathematics that studies algebraic structures themselves, not examples ("models")... 24 KB (2,951 words) - 18:28, 20 January 2024 |
based on the number of operations they use and the laws they follow. Universal algebra constitutes a further level of generalization that is not limited... 120 KB (11,895 words) - 22:58, 8 April 2024 |
In universal algebra, a variety of algebras or equational class is the class of all algebraic structures of a given signature satisfying a given set of... 13 KB (1,904 words) - 03:14, 20 January 2024 |
In universal algebra, an abstract algebra A is called simple if and only if it has no nontrivial congruence relations, or equivalently, if every homomorphism... 2 KB (212 words) - 14:01, 6 March 2022 |
In mathematics, the universal enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the... 52 KB (8,897 words) - 06:44, 23 December 2023 |
a quotient algebra is the result of partitioning the elements of an algebraic structure using a congruence relation. Quotient algebras are also called... 10 KB (1,427 words) - 07:09, 29 January 2023 |
In universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure... 20 KB (2,675 words) - 12:17, 9 April 2024 |
Isomorphism theorems (section Universal algebra) Lie algebras, and various other algebraic structures. In universal algebra, the isomorphism theorems can be generalized to the context of algebras and... 25 KB (3,424 words) - 11:27, 10 January 2024 |
In universal algebra, a basis is a structure inside of some (universal) algebras, which are called free algebras. It generates all algebra elements from... 12 KB (1,955 words) - 22:27, 9 May 2022 |