What is the common link, if there is any, between Church-Rosser systems,prefix codes with bounded synchronization delay, and local Rees extensions? Thefirst obvious answer is that each of these notions relates to topics ofinterest for WORDS: Church-Rosser systems are certain rewriting systems overwords, codes are given by sets of words which form a basis of a free submonoidin the free monoid of all words (over a given alphabet) and local Reesextensions provide structural insight into regular languages over words. So, itseems to be a legitimate title for an extended abstract presented at theconference WORDS 2017. However, this work is more ambitious, it outlines someless obvious but much more interesting link between these topics. This link isbased on a structure theory of finite monoids with varieties of groups and theconcept of local divisors playing a prominent role. Parts of this work appearedin a similar form in conference proceedings where proofs and further materialcan be found.
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