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In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid operation and with the unique sequence of zero elements, often called the empty string and denoted by ε or λ, as the identity element. The free monoid on a set A is usually denoted A∗. The free semigroup on A is the subsemigroup of A∗ containing all elements except the empty string. It is usually denoted A+.

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  • Volný monoid (cs)
  • Monoid bebas (in)
  • Free monoid (en)
  • Monoide livre (pt)
  • 自由么半群 (zh)
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  • Em álgebra abstrata, o monoide livre sobre um conjunto A é o monoide cujos elementos são todas as strings (ou sequências de caracteres) finitas formadas por zero ou mais elementos de A. Ele é normalmente denotado por A∗. O elemento de identidade é a única sequência com zero elementos, muitas vezes chamada de string vazia e denotada por ε ou λ, e a operação do monoide é a concatenação de strings. O semigrupo livre em A é o subsemigrupo de A∗ contendo todos os elementos exceto a string vazia. Ele é denotado geralmente por A+. (pt)
  • 在抽象代數裡,於一集合A上的自由幺半群是指一幺半群,其元素都是由A內零個或多個元素以串接之二元運算形成的有限序列(或字符串)。通常標記為A*。其單位元為空字元串,標記為ε 或 λ。在A上的自由半群則指是A*內的子半群,其包含除了空字串外的所有元素。通常標記為A+。 更一般地,一抽象幺半群(半群)S被稱做是自由的,若其與某一集合上的自由幺半群(半群)同構。 如其名稱所述,自由幺半群(半群)為滿足定義了自由对象的泛性質的物件,在幺半群(半群)的範疇裡。它允許每一個么半群(半群)都會是某一自由幺半群(半群)的同態映像。研究半群為自由半群的映像的學科稱做。 (zh)
  • 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+. (cs)
  • In abstract algebra, the free monoid on a set is the monoid whose elements are all the finite sequences (or strings) of zero or more elements from that set, with string concatenation as the monoid operation and with the unique sequence of zero elements, often called the empty string and denoted by ε or λ, as the identity element. The free monoid on a set A is usually denoted A∗. The free semigroup on A is the subsemigroup of A∗ containing all elements except the empty string. It is usually denoted A+. (en)
  • Dalam aljabar abstrak, monoid bebas pada himpunan adalah monoid yang semua elemennya adalah (atau string) dari nol atau lebih elemen dari himpunan, dengan sebagai operasi monoid dan dengan urutan unik elemen nol, sering disebut dan dilambangkan dengan ε atau λ, sebagai elemen identitas. Monoid bebas pada himpunan A biasanya dilambangkan A∗. Semigrup bebas di A adalah subsemigrup dari A∗ mengandung semua elemen kecuali string kosong. Biasanya dilambangkan A+. (in)
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