Noun
That branch of mathematics which treats of the relations and properties of quantity by means of letters and other symbols. It is applicable to those relations that are true of every kind of magnitude.
A treatise on this science.
Source: Webster's dictionaryAbstract algebra Abstract algebra employs several types of sequences, including sequences of mathematical objects such as groups or rings. Source: Internet
A basis of a Hilbert space is not the same thing as a basis in the sense of linear algebra above. Source: Internet
A basis, then, is a set of generators being a basis of the Lie algebra in the usual vector space sense. Source: Internet
A C*-algebra is a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: * A is a topologically closed set in the norm topology of operators. Source: Internet
A Boolean algebra with only one element is called a trivial Boolean algebra or a degenerate Boolean algebra. Source: Internet
A closer non-commutative analog are central simple algebras (CSAs) – ring extensions over a field, which are simple algebra (no non-trivial 2-sided ideals, just as for a field) and where the center of the ring is exactly the field. Source: Internet