[[환,ring]] [[이론,theory]]

Sub:
[[국소환,local_ring]]
[[다항식환,polynomial_ring]]
[[부분환,subring]]
[[semiring]] =,semiring =,semiring . semiring
{
KmsE:semiring

반환?
준환?
세미환?

...에서 [[뺄셈,subtraction]]만 제외? chk

Sub:
[[star_semiring]] =,star_semiring =,star_semiring . star_semiring
{
https://en.wikipedia.org/wiki/Semiring#Star_semirings
"A star semiring (sometimes spelled starsemiring) is a semiring with an additional unary operator *, satisfying a^^*^^ = 1 + a a^^*^^ = 1 + a^^*^^ a. A [[클레이니_대수,Kleene_algebra]] is a '''star semiring''' with idempotent addition and some additional axioms."
}

Ndict:semiring
Bing:semiring
Ggl:semiring
}

[[환,ring]] =환,ring =,ring 환 ring
{

Sub:
[[불_환,Boolean_ring]]

MKL
[[영인자,zero_divisor]]


bmks ko
환(ring)에서 체(field)까지 - 1. 환(ring) :: jjycjn's Math Storehouse
https://jjycjnmath.tistory.com/228

twins
[[Libre:환_(수학)]]
= https://librewiki.net/wiki/환_%28수학%29

[[Namu:환(대수학)]]
= https://namu.wiki/w/환%28대수학%29

[[WpKo:환_(수학)]]
= https://ko.wikipedia.org/wiki/환_(수학)
= https://ko.wikipedia.org/wiki/환_%28수학%29
 인접분야 - universal_enveloping_algebra / [[homological_algebra]] =,homological_algebra =,homological_algebra . homological_algebra { WtEn:homological_algebra WpKo:호몰로지_대수학 [[WpEn:homological_algebra]] = https://en.wikipedia.org/wiki/Homological_algebra }

}

[[나눗셈환,division_ring]] =,division_ring . division_ring
{

division ring
0이 아닌 모든 원소가 [[가역원]]인 환?
https://en.wiktionary.org/wiki/division_ring
https://en.wikipedia.org/wiki/Division_ring
[[https://terms.naver.com/entry.naver?docId=4125193&cid=60207&categoryId=60207 수학백과 나눗셈환]]
Ndict:나눗셈환
Bing:나눗셈환
Bing:"division ring"


"division ring"

MKL [[나눗셈,division]]

Up: [[nontrivial_ring]]
}

[[trivial_ring]] =,trivial_ring =,trivial_ring . trivial_ring
{
trivial ring
자명환 (wk)
https://ko.wikipedia.org/wiki/자명환

WtEn:trivial_ring ?

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

"trivial ring"
Ggl:"trivial ring"
}
//위아래cmp

[[nontrivial_ring]] =,nontrivial_ring =,nontrivial_ring . nontrivial_ring
{
nontrivial ring

Ndict:"nontrivial ring"
Ggl:"nontrivial ring"
Bing:"nontrivial ring"

}

[[ordered_ring]] =,ordered_ring =,ordered_ring . ordered_ring
{
[[commutative_ring]]이면서 [[total_order]]ing을 가진.
WtEn:ordered_ring
https://planetmath.org/orderedring
}

[[commutative_ring]] =,commutative_ring =,commutative_ring . commutative_ring
{

https://mathworld.wolfram.com/CommutativeRing.html
}

Topics:
[[소아이디얼,prime_ideal]]
{
ideal - 아이디얼 or 이데알... pagename TBD

[[WpKo:아이디얼]]
 = https://ko.wikipedia.org/wiki/아이디얼
[[WpEn:Ideal_(ring_theory)]]
 = https://en.wikipedia.org/wiki/Ideal_%28ring_theory%29
}

= Cmp =
[[군론,group_theory]]

----
Twins:
WpKo:환론