Editing Free monoid (section)

===Codes===
A set of free generators for a free monoid ''P'' is referred to as a '''basis''' for '''P''': a set of words ''C'' is a '''code''' if ''C''* is a free monoid and ''C'' is a basis.<ref name=Lot5/>  A set ''X'' of words in ''A''<sup>&lowast;</sup> is a '''prefix''', or has the '''prefix property''', if it does not contain a proper [[prefix (computer science)|(string) prefix]] of any of its elements<!--- deleted, since "≤" as shorthand for "string prefix of" has not been defined yet, and is not used elsewhere in the article: that is, ''x'',''y'' in ''X'' with ''x'' ≤ ''y'' implies ''x'' = ''y''--->.  Every prefix in ''A''<sup>+</sup> is a code, indeed a [[prefix code]].<ref name=Lot5/><ref name=BPR58>{{harvtxt|Berstel|Perrin|Reutenauer|2010|p=58}}</ref>

A submonoid ''N'' of ''A''<sup>&lowast;</sup> is '''right unitary''' if ''x'', ''xy'' in ''N'' implies ''y'' in ''N''.  A submonoid is generated by a prefix if and only if it is right unitary.<ref name=Lot15>{{harvtxt|Lothaire|1997|p=15}}</ref>