The word 'algebra' is used for various branches and structures of mathematics.
The term is also traditionally used for the field of: An "algebra", or to be verbose, an algebra over a field, is a vector space equipped with a bilinear vector product.
Some notable algebras in this sense are: See also coalgebra, the dual notion.
A different class of "algebras" consists of objects which generalize logical connectives, sets, and lattices.
"Algebra" can also describe more general structures: