환,ring 이론,theory

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

반환?
준환?
세미환?

...에서 뺄셈,subtraction만 제외? chk

MKL semigroup

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."
}

semiring
semiring
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
환_(수학)
= https://librewiki.net/wiki/환_(수학)

환(대수학)
= https://namu.wiki/w/환(대수학)

환_(수학)
= https://ko.wikipedia.org/wiki/환_(수학)
= https://ko.wikipedia.org/wiki/환_(수학)
}

나눗셈환,division_ring =,division_ring . division_ring
{

division ring
0이 아닌 모든 원소가 가역원인 환?
https://en.wiktionary.org/wiki/division_ring
https://en.wikipedia.org/wiki/Division_ring
수학백과 나눗셈환
나눗셈환
나눗셈환
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

trivial_ring ?

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

"trivial ring"
trivial ring
}
//위아래cmp

nontrivial_ring =,nontrivial_ring =,nontrivial_ring . nontrivial_ring
{
nontrivial ring

nontrivial ring
nontrivial ring
nontrivial ring

}

ordered_ring =,ordered_ring =,ordered_ring . ordered_ring
{
commutative_ring이면서 total_ordering을 가진.
ordered_ring
https://planetmath.org/orderedring
}

commutative_ring =,commutative_ring =,commutative_ring . commutative_ring
{

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

유클리드_환,Euclidean_ring

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

아이디얼
Ideal_(ring_theory)
}