Problems formulated with adjoint functors 1.3 Adjoint functors as solving optimization problems 1.4 The case of partial orders 2 Formal definitions...

Lie algebra by A L . Construction of the universal enveloping algebra attempts to reverse this process: to a given Lie algebra L over K we find the...

Set (with the monoidal structure induced by the cartesian product) is a monoid in the usual sense. A monoid object in Top (with the monoidal struct...

Similarly, the requirement for the ring multiplication to be associative is sometimes dropped, and rings in which the associative law holds are the...

In abstract algebra , a free algebra is the noncommutative analogue of a polynomial ring (which may be regarded as a free commutative algebra ). Le...

Rng : a ring lacking a multiplicative identity. Commutative ring : a ring with commutative multiplication. Boolean ring : a commutative ring with i...

Formal definitions and algebraic properties 2.1 Anticommutativity of the wedge product 2.2 The exterior power 2.2.1 Basis and dimension 2.3 Graded ...

Distinction with symmetric tensors The symmetric algebra and symmetric tensors are easily confused: the symmetric algebra is a quotient of the tens...

If e is both a left identity and a right identity, then it is called a two-sided identity , or simply an identity . An identity with respect to add...