Algebras have elements, such as integers. Algebras have operations on elements, such as addition. Integer additions result in integers. Integer addition commutes: 13 + 27 = 40 = 27 + 13. Integer addition is associative: (13 + 27) + 5 = 45 = 13 + (27 + 5). Integer identity element adds to integers to make the same integer: 13 + 0 = 13, and 0 + 0 = 0. Integer inverse elements add to integers to make zero: 13 + -13 = 0, and 0 + 0 = 0. Finite or infinite tables can show operation results for all element pairs.
If elements are colors and operation is additive color mixing, adding two colors makes color, by wavelength-space vector addition, following Grassmann's laws {algebra and color}. Order of adding two colors does not matter, so color addition is commutative. Sequence of adding three colors does not matter, so color addition is associative. Colors have complementary additive-inverse colors, and adding both colors makes white, so color addition has inverses. Adding black, white, or gray to color does not change color hue but does change saturation, so black, white, or gray are like identity elements. Unlike integer addition, adding color to itself makes same color.
distributive property
Identity, inverse, commutation, and association work whether colors come from light sources or reflect from pigments. Colors from light sources and colors from pigment reflections can mix. If reflected color mixes with mixture of two source colors, or if reflected color mixes with each of two source colors and then mixtures combine, same color results, like the distributive property.
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Date Modified: 2022.0224