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A scalar multiplication operator A set (or domain) Note that the zero element (i.e. the element that represents the absence of an edge in the graph) can also be reinterpreted. [26]: "VII. 0-Element: No Graph Edge" For example, the following algebras can be implemented in GraphBLAS:
In algebra, the zero-product property states that the product of two nonzero elements is nonzero. In other words, =, = = This property is also known as the rule of zero product, the null factor law, the multiplication property of zero, the nonexistence of nontrivial zero divisors, or one of the two zero-factor properties. [1]
The math template formats mathematical formulas generated using HTML or wiki markup. (It does not accept the AMS-LaTeX markup that <math> does.) The template uses the texhtml class by default for inline text style formulas, which aims to match the size of the serif font with the surrounding sans-serif font (see below).
A zero morphism in a category is a generalised absorbing element under function composition: any morphism composed with a zero morphism gives a zero morphism. Specifically, if 0 XY : X → Y is the zero morphism among morphisms from X to Y , and f : A → X and g : Y → B are arbitrary morphisms, then g ∘ 0 XY = 0 XB and 0 XY ∘ f = 0 AY .
The most well known example of an absorbing element comes from elementary algebra, where any number multiplied by zero equals zero. Zero is thus an absorbing element. The zero of any ring is also an absorbing element. For an element r of a ring R, r0 = r(0 + 0) = r0 + r0, so 0 = r0, as zero is the unique element a for which r − r = a for any ...
For any element x in a ring R, one has x0 = 0 = 0x (zero is an absorbing element with respect to multiplication) and (–1)x = –x. If 0 = 1 in a ring R (or more generally, 0 is a unit element), then R has only one element, and is called the zero ring. If a ring R contains the zero ring as a subring, then R itself is the zero ring. [6]