multiplicative identity

multiplicative identity

[‚məl·tə′plik·əd·iv ī′den·əd·ē]
(mathematics)
In a mathematical system with an operation of multiplication, denoted ×, an element 1 such that 1 × e = e × 1 = e for any element e in the system.
References in periodicals archive ?
One candidate for e that exists in every semiring is the multiplicative identity 1.
Clearly all the properties of a semiring are satisfied where 0 is the additive identity and + 1 is multiplicative identity. Here + 1 and -1 are the units of S.
In mathematics, a multiplicative inverse for a number X is a number that when multiplied by X yields the multiplicative identity, 1.
By (1) and (2) [u.sub.e] is a multiplicative identity of A [[??].sup.[sigma].sub.[alpha]] G and by (3) the multiplication on A [[??].sup.[sigma].sub.[alpha]] G is associative.
By (7), (8), and (9) it follows that A [[??].sup.[sigma].sub.[alpha]] G has a multiplicative identity if and only if ob(G) is finite; in that case the multiplicative identity is [[summation].sub.e[member of]ob(G)] [u.sub.e].
The multiplicative identity property keeps quant ities the same: 1 x 10) = 10.

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