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单词 Monoid
释义

monoid


A monoid is a semigroupPlanetmathPlanetmath G which contains an identity elementMathworldPlanetmath; that is, there exists an element eG such that ea=ae=a for all aG.

If e and f are identity elements of a monoid G, then e=ef=fe=f, so we may speak of “the” identity element of G.

A monoid homomorphism from monoids G to H is a semigroup homomorphism f:GH such that f(eG)=eH, where eG,eH are identity elements of G and H respectively.

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更新时间:2025/5/4 17:08:30