Congruence preserving functions on free monoids

被引：3
|
作者：
Cegielski, Patrick [1 ]
Grigorieff, Serge [2 ,3 ]
Guessarian, Irene [2 ,3 ,4 ]
机构：
[1] Univ Paris Est Creteil, IUT Senart Fontainebleau, EA 4219, LACL, Creteil, France
[2] CNRS, UMR 8243, IRIF, Paris, France
[3] Univ Paris 07, Paris, France
[4] UPMC Univ Paris 6, Paris, France
来源：
ALGEBRA UNIVERSALIS | 2017年 / 78卷 / 03期
关键词：
congruence preservation; free monoid; affine completeness;
D O I：
10.1007/s00012-017-0464-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 for some finite sequence of words . 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.
引用
收藏
页码：389 / 406
页数：18
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