Basis (universal Algebra)

Basis (universal Algebra)

In universal algebra a basis is a structure inside of some (universal) algebras, which are called free algebras. It generates all algebra elements from its own elements by the algebra operations in an independent manner. It also represents the endomorphisms of an algebra by certain indexings of algebra elements, which can correspond to the usual matrices when the free algebra is a vector space.

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Basis (universal Algebra) - Examples - Word Monoid
... Let be an alphabet" namely a usually finite)set of objects called letters" ... Let W denote the corresponding set of words or strings" which will be denoted as in strings,namely either by writing their letters in sequence or by in case of the empty word Formal Language notation) ... Accordingly,the juxtaposition will denote the concatenation of two words v and w,namely the word that begins with v and is followed by w ...

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