//eom
semigroup with identity

//wpko
[[항등원,identity_element]]을 갖는
[[결합법칙,associativity]]을 따르는
[[이항연산,binary_operation]]을 갖춘 [[대수구조,algebraic_structure]].

i.e.
"추상대수학에서 '''모노이드'''는 [[항등원,identity_element]]을 갖는, [[결합법칙,associativity]]을 따르는 [[이항연산,binary_operation]]을 갖춘 [[대수구조,algebraic_structure]]이다. [[군,group]]의 정의에서 [[역원,inverse_element]]의 존재를 생략하거나, [[반군,semigroup]]([[semigroup]])의 정의에서 [[항등원,identity_element]]의 존재를 추가하여 얻는다."
<<tableofcontents>>
= Sub =

== trivial monoid ==
trivial_monoid
WpEn:Trivial_monoid

via
 [[trivial_group]] - [[군,group]]

cmp
 [[trivial_group]]
 [[trivial_ring]]

Up: [[trivial]]

== free monoid ==
[[free_monoid]] =,free_monoid . free_monoid
{

WtEn:free_monoid

https://encyclopediaofmath.org/wiki/Free_semi-group
 ''(Redirected from Free monoid)''
[[단어,word]]
[[알파벳,alphabet]]

}
== monoid object ==
[[모노이드대상,monoid_object]] - [[대상,object]]

Ndict:"monoid object"
Ggl:"monoid object"

== monoidal category ==
[[모노이드범주,monoidal_category]] - [[범주,category]]
 [[closed_monoidal_category]]

Ndict:"monoidal category"
Ggl:"monoidal category"

=== closed monoidal category ===
Ggl:"closed monoidal category"

== submonoid ==
submonoid
=,submonoid . submonoid 
부분 모노이드
[[부분모노이드,submonoid]]
https://mathworld.wolfram.com/Submonoid.html
Ndict:submonoid 
Ggl:submonoid 

= Topics: =

= MKL =
[[semigroup]] - [[반군,semigroup]](잠정적pagename)
[[항등원,identity_element]] // semigroup + 항등원 => '''모노이드'''

Cmp [[모나드,monad]]

= Inter =
https://artofproblemsolving.com/wiki/index.php/Monoid

https://mathworld.wolfram.com/Monoid.html

https://everything2.com/title/monoid

https://groupprops.subwiki.org/wiki/Monoid

https://encyclopediaofmath.org/wiki/Monoid

[[WpKo:모노이드]]
= https://ko.wikipedia.org/wiki/모노이드

https://ncatlab.org/nlab/show/monoid

... Google:monoid Naver:monoid
... Google:모노이드 Naver:모노이드

Up:
[[추상대수,abstract_algebra]]