Assertion: algebra | /r/CapableOf | satisfy axiom
Facets:
value: from the algebra of integers
type: OTHER
Source sentences:
text: Thus, an algebra is an algebraic structure, which consists of a set, together with operations of multiplication, addition, and scalar multiplication by elements of the underlying field, and satisfies the axioms implied by "vector space" and "bilinear".
text: If on the other hand we can show how to construct any algebra satisfying the axioms from the algebra of integers, limiting ourselves only to certain algebraic constructions, then by a theorem of Birkhoff applicable to those constructions we can infer that the axiomatization is complete.