Assertion: algebra | /r/HasProperty | unitary
Facets:
Source sentences:
text: An algebra is unital or unitary if it has an identity element with respect to the multiplication.
text: An algebra is unital or unitary if it has a unit or identity element I with Ix = x = xI for all x in the algebra.
text: Algebras over a field can be viewed as F-algebras of signature 1 + 1 + A + A×A + A×A + k×A over the category of sets, of signature 1 + A×A over the category of modules (a module with an internal multiplication), and of signature k×A over the category of rings (a ring with a scalar multiplication), when they are associative and unitary.