Volný monoid

Volný monoid na množině je v abstraktní algebře monoid, jehož prvky jsou všechny konečné posloupnosti (neboli řetězce) prvků této množiny, přičemž monoidovou operací je operace zřetězení a neutrální prvek tvořený posloupností nula prvků se nazývá prázdný řetězec, a označuje se obvykle ε nebo λ. Volný monoid nad množinou A se obvykle označuje A∗; volná pologrupa na A je podpologrupa A∗ obsahující všechny prvky kromě prázdného řetězce; obvykle se označuje A+.[1][2]

Obecněji, abstraktní monoid (nebo pologrupu) S nazýváme volný nebo volná, jestliže je izomorfní s volným monoidem (nebo pologrupou) nad nějakou množinou[1].

Jak jméno naznačuje, volné monoidy a pologrupy jsou objekty které vyhovují obvyklé univerzální vlastnosti definující volné objekty v kategorii monoidů nebo pologrup. Z toho plyne, že každý monoid (resp. každá pologrupa) se je homomorfním obrazem volného monoidu (resp. volné pologrupy). Studium pologrup jako obrazů volných pologrup se nazývá kombinatorická teorie pologrup.

Odkazy

Reference

V tomto článku byl použit překlad textu z článku Free monoid na anglické Wikipedii.

  1. ↑ a b LOTHAIRE, M. Combinatorics on words. 2. vyd. Svazek 17. [s.l.]: Cambridge University Press, 1997. (Cambridge Mathematical Library). Dostupné online. ISBN 0-521-59924-5. DOI 10.1017/CBO9780511566097. 
  2. ↑ PYTHEAS FOGG, N. Substitutions in dynamics, arithmetics and combinatorics. Svazek 1794. Berlin: Springer-Verlag, 2002. (Lecture Notes in Mathematics). ISBN 3-540-44141-7. 

Literatura

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