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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]
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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 .
These templates shows a chess diagram, a graphic representation of a position in a chess game, using standardised symbols resembling the pieces of the standard Staunton chess set. The default template for a standard chess board is {{ Chess diagram }} .
the group under multiplication of the invertible elements of a field, [1] ring, or other structure for which one of its operations is referred to as multiplication. In the case of a field F, the group is (F ∖ {0}, •), where 0 refers to the zero element of F and the binary operation • is the field multiplication, the algebraic torus GL(1).
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 r in the ring R. This property holds true also in a rng since multiplicative identity isn't required.