Sentence examples for multiplicative identity of from inspiring English sources

The additive identity and multiplicative identity of R ( J ) are defined by 0 ¯ and 1 ¯ respectively.

The multiplicative identity of ( FS _{A_p,rho }^{*,infty }(mathbb R^{2d};B)) is given by (mathbf {1}).

If there exists some (ein E) such that (ex =xe=x) for each (xin E) then e is called a unit (i.e., a multiplicative identity) of E.

K is nonempty closed, and ({theta,e}subset X ) (where θ is null, and e is the multiplicative identity of the Banach space X); (aK+bK subset K) for any nonnegative a, b; (K^{2}=KKsubset K); and.

A subset K of X is called a cone if the following are true: (i) K is nonempty closed, and ({theta,e}subset X ) (where θ is null, and e is the multiplicative identity of the Banach space X);   (ii) (aK+bK subset K) for any nonnegative a, b;   (iii) (K^{2}=KKsubset K); and   (iv) ((K) cap -K) ={theta}).  .

If there exists an element e such that (xcirc e=ecirc x=x) for all (xinmathcal{J}), then e is called the multiplicative identity element of EJA.

In some contexts, such as the integers, distributivity over addition and the existence of a multiplicative identity is enough to uniquely determine the multiplication operation.

There is only one such possible tiling, the empty tiling, and we assign it a score of 1 because it is the multiplicative identity.

Let be the (real) unital extension of (see Section 2) and 1 the multiplicative identity element in.

With no generators the free monoid, free group, and free ring are all the one-element algebra consisting of just the additive identity 0. A ring with identity means having a multiplicative identity, that is, a word ε.

The additive identity and multiplicative identity in are denoted by and, respectively.