환론,ring_theory

Difference between r1.12 and the current

@@ -14,6 +14,15 @@

...에서 [[뺄셈,subtraction]]만 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."
}
Ndict:semiring
Bing:semiring
Ggl:semiring
@@ -23,23 +32,7 @@
{

Sub:
[[불_환,Boolean_ring]] =불_환,Boolean_ring =,Boolean_ring 불_환 Boolean_ring
{
 
WtEn:Boolean_ring ?
 
MKL
[[ring_sum_normal_form]] =,ring_sum_normal_form =,ring_sum_normal_form . ring_sum_normal_form { '''ring sum normal form (RSNF or RNF)''' WtEn:ring_sum_normal_form WpEn:Ring_sum_normal_form "ring sum normal form" Ggl:"ring sum normal form" - syn. [[algebraic_normal_form]](wten) }
[[algebraic_normal_form]] =,algebraic_normal_form =,algebraic_normal_form . algebraic_normal_form { '''algebraic normal form (ANF)''' [[WtEn:algebraic_normal_form]] = https://en.wiktionary.org/wiki/algebraic_normal_form (syn. [[ring_sum_normal_form]]) [[WpEn:algebraic_normal_form]] = https://en.wikipedia.org/wiki/Algebraic_normal_form }
[[Zhegalkin_polynomial]] =,Zhegalkin_polynomial =,Zhegalkin_polynomial . Zhegalkin_polynomial { '''Zhegalkin polynomial''' WtEn:Zhegalkin_polynomial WpEn:Zhegalkin_polynomial Ggl:"Zhegalkin polynomial" Ndict:"Zhegalkin polynomial" Naver:"Zhegalkin polynomial" "Zhegalkin polynomial" Up: [[다항식,polynomial]]}
 
[[WtEn:Boolean_ring]]
= https://en.wiktionary.org/wiki/Boolean_ring
 
[[WpEn:Boolean_ring]]
 
 
}
[[불_환,Boolean_ring]]

MKL
[[영인자,zero_divisor]]
@@ -121,6 +114,9 @@
https://mathworld.wolfram.com/CommutativeRing.html
}

[[유클리드_환,Euclidean_ring]]
 
----
Topics:
[[소아이디얼,prime_ideal]]
{




반환?
준환?
세미환?

...에서 뺄셈,subtraction만 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."
}


환,ring =환,ring =,ring 환 ring
{




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




나눗셈환,division_ring =,division_ring . division_ring
{



"division ring"



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



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

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


}

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

commutative_ring =,commutative_ring =,commutative_ring . commutative_ring
{




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