185:. In the case of a semiring with 0, the definition of an absorbing element is sometimes relaxed so that it is not required to absorb 0; otherwise, 0 would be the only absorbing element.
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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.
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arithmetics as defined in IEEE-754 standard contains a special value called Not-a-Number ("NaN"). It is an absorbing element for every operation; i.e.,
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may, quite naturally, denote the neutral element of a monoid. In this article "zero element" and "absorbing element" are synonymous.
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Kilp, M.; Knauer, U.; Mikhalev, A.V. (2000), "Monoids, Acts and
Categories with Applications to Wreath Products and Graphs",
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on that set. The result of combining an absorbing element with any element of the set is the absorbing element itself. In
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