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- W2514304517 abstract "A function on an algebra is congruence preserving if for any congruence, it maps congruent elements to congruent elements. We show that on a free monoid generated by at least three letters, a function from the free monoid into itself is congruence preserving if and only if it is of the form $${x mapsto w_{0}xw_{1} cdots w_{n-1}xw_n }$$ for some finite sequence of words $${w_0,ldots ,w_n}$$ . We generalize this result to functions of arbitrary arity. This shows that a free monoid with at least three generators is a (noncommutative) affine complete algebra. As far as we know, it is the first (nontrivial) case of a noncommutative affine complete algebra." @default.
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- W2514304517 date "2017-10-20" @default.
- W2514304517 modified "2023-10-15" @default.
- W2514304517 title "Congruence preserving functions on free monoids" @default.
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- W2514304517 doi "https://doi.org/10.1007/s00012-017-0464-x" @default.
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