앨지브라,algebra



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1. Sub

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1.1. elementary *

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1.2. Boolean algebra

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1.2.1. + complete Boolean algebra

Boolean_algebra =,Boolean_algebra . Boolean_algebra
{
See VG 불_대수,Boolean_algebra / MK 불_대수,Boolean_algebra


Boolean_algebra_expression = 불_식,Boolean_expression ? chk
WtEn:boolean_expression
complete_Boolean_algebra
완전인가 완비인가
https://en.wikipedia.org/wiki/Complete_Boolean_algebra

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1.2.2. free Boolean algebra

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1.3. collapsing algebra

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1.4. algebra of sets

algebra_of_sets =,algebra_of_sets . algebra_of_sets
algebra of sets
https://en.wikipedia.org/wiki/Algebra_of_sets
https://encyclopediaofmath.org/wiki/Algebra_of_sets
"Also called Boolean_algebra or field_of_sets { https://encyclopediaofmath.org/wiki/Field_of_sets } by some authors. "

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1.5. algebra of a field AKA k-algebra

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1.6. sigma-algebra / σ-algebra


}

sigma에 대해: curr see VG:시그마대수,sigma-algebra#s-3 #"이름의 sigma에 대한 설명"

비슷한 느낌의 이름(?)인
F대수,F-algebra {

bmks en
Understanding F-Algebras - School of Haskell | School of Haskell
https://www.schoolofhaskell.com/user/bartosz/understanding-algebras


WpEn:F-algebra (여기선 F-algebra) ........대문자 slanted ??
https://encyclopediaofmath.org/wiki/F-algebra ....(여기선 f-algebra) ...... 소문자 italic ??
(임시, 검색:) https://ncatlab.org/nlab/search?query=f-algebra
....
Ggl:f-algebra
}
l대수,l-algebra {
curr see: https://encyclopediaofmath.org/wiki/F-algebra
...
Ggl:l-algebra
}
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1.7. Weyl algebra

Weyl_algebra =,Weyl_algebra . Weyl_algebra
{
https://en.wikipedia.org/wiki/Weyl_algebra
https://ko.wikipedia.org/wiki/바일_대수
Weyl+algebra
}

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1.8. *-algebra / involutive algebra

*-algebra // star-algebra ?? .... cf. https://mathworld.wolfram.com/C-Star-Algebra.html = WpEn:C*-algebra
involutive_algebra
=,*-algebra =,star-algebra =,involutive_algebra .
involutive algebra
https://en.wikipedia.org/wiki/*-algebra
WpKo:대합_대수 = https://ko.wikipedia.org/wiki/대합_대수
MKL involution =,involution . involution { 인볼루션 대합 (??) (wk) 매우 간단한 개념. 연산,operation 연산자,operator 주기,period 둘,two ... https://mathworld.wolfram.com/Involution.html WpKo:대합_(수학) = https://ko.wikipedia.org/wiki/대합_(수학) involution }

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1.9. symmetric algebra

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1.10. process algebra

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1.11. Witt algebra

Witt_algebra =,Witt_algebra =,Witt_algebra . Witt_algebra
{
Witt algebra
// named after Ernst Witt

KmsE:witt - 위트 - 같은사람? https://en.wikipedia.org/wiki/Ernst_Witt -> https://en.wikipedia.org/wiki/Witt's_theorem 같은사람임. 근데 위트? "was a German mathematician" 비트가 맞지 않을까? https://ko.wikipedia.org/wiki/에른스트_비트


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1.12. Lie algebra

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1.13. De Morgan algebra ( + Ockham algebra + Kleene algebra )

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1.14. Stone algebra

Stone_algebra =,Stone_algebra . Stone_algebra
Stone algebra


"Stone algebra"
Ggl:Stone algebra

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1.15. Hurwitz algebra

Hurwitz_algebra =,Hurwitz_algebra . Hurwitz_algebra
{
Hurwitz algebra


rel
Hurwitz_problem

"Hurwitz algebra"
}

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1.16. composition algebra

composition_algebra =,composition_algebra . composition_algebra
{
composition algebra
합성대수 ?




"composition algebra"
Ggl:composition algebra

}



#divalg
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1.17. division algebra

나눗셈대수,division_algebra
=나눗셈대수,division_algebra =,division_algebra . 나눗셈대수 division_algebra
{
division algebra



WtEn:division_algebra
= https://en.wiktionary.org/wiki/division_algebra
  1. A linear algebra such that its non-zero vectors form a multiplicative_group.
  2. An algebra over a field such that every non-zero element of it has a multiplicative inverse. (It is not required to have a unity element( Ggl:unity element ).)

WpEn:Division_algebra
= https://en.wikipedia.org/wiki/Division_algebra




Ndict:division algebra
at 2023-08-19 - 사원수,quaternion { WtEn:quaternion KmsE:quaternion VG: 사원수,quaternion } 팔원수,octonion =팔원수,octonion =,octonion { octonion KmsE:octonion WtEn:octonion Ndict:팔원수 https://ko.wikipedia.org/wiki/팔원수 https://en.wikipedia.org/wiki/Octonion Ggl:octonion } 에 대한 수학백과 항목 두 곳에서만 언급중.


} // "division algebra" .... Ggl:division algebra


#assoc_alg
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1.18. associative algebra

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1.19. non-associative algebra

non-associative_algebra (w)
=,non-associative_algebra . non-associative_algebra

AKA distributive algebra = distributive_algebra =,distributive_algebra .
"or distributive algebra"



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1.20. power-associative algebra

power-associative_algebra =,power-associative_algebra . power-associative_algebra

power-associative algebra




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1.21. differential algebra

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1.22. Poisson algebra

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1.23. tensor algebra

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1.24. bialgebra

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1.25. quasi-bialgebra

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1.26. Hopf algebra

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1.27. coalgebra

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1.28. cofree coalgebra

cofree_coalgebra =,cofree_coalgebra . cofree_coalgebra
WtEn:cofree_coalgebra
cofree coalgebra
https://en.wikipedia.org/wiki/Cofree_coalgebra

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1.29. measuring coalgebra

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1.30. free algebra

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1.31. Jordan algebra

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1.32. alternative algebra

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1.33. commutative *

commutative algebra = commutative_algebra =,commutative_algebra . commutative_algebra |=,commalg .




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1.34. action algebra

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1.35. information * / valuation *

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1.36. ADDHERE

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1.37. ADDHERE

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1.38. ADDHERE

ADDHERE
ADDHERE

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2. Sub (-algebra 외)

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2.1. Galois theory

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2.2. algebraic propositional logic

algebraic_propositional_logic =,algebraic_propositional_logic =,algebraic_propositional_logic . algebraic_propositional_logic (local에도 writing)


//copied from VG:명제논리,propositional_logic
https://plato.stanford.edu/entries/logic-algebraic-propositional/
{
algebraic_propositional_logic (w) . Sub? 앞에 algebraic이 붙으면 달라지는 것은? QQQ


algebraic propositional logic


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2.3. algebra system

혹시 CAS가 아닌 algebra system이 있는지... 글쎄?

aka computer_algebra ?? (그냥 생각)

aka algebraic_system ?? (그냥생각, 아닐 듯)

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2.3.1. computer algebra system (CAS)

컴퓨터대수시스템 ?
computer algebra system
computer_algebra_system =,computer_algebra_system . computer_algebra_system |=,CAS CAS
CAS
WtEn:CAS
WtEn:computer_algebra_system
WpSp:Computer_algebra_system ?
WpEn:Computer_algebra_system ?
Computer_algebra_system

Rel.
symbolic_computation?
symbolic_computing?
아무튼
symbolic_ 등등 과 관련... 왜냐?
실제 수,number보단 기호,symbol 심벌,symbol을 manipulation의 대상으로 사용.
rel. symbolic_logic ...

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2.3.1.1. 각종 CAS systems

Ex. / Sub:
매트랩,MATLAB
옥타브,Octave .... MATLAB_and_Octave curr. VG:MATLAB_and_Octave
Xcas =,Xcas . Xcas - Giac의 UI라고 함.
{


Giac =,Giac . Giac
{
free/opensource CAS.


이것들은 notebook_interface를 쓰는 일이 많음.... WtEn:notebook_interface ?

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2.4. algebraic geometry

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3. 표현들

표현 '대수학': 학문 분야임을 명확히 나타냄
(대수학을 줄여 대수로 부르기도 함)
하지만 '대수학'이 아닌 '대수'도 따로 있음. 대수학에서 다루는 대상,object.

표현 '대수':
'대수학'의 줄임말일 수도 있고 아닐 수도 있음. tbw

[https]수학백과: 가측 공간 처음부분 참조

Suffix -대수:

학문 분야명으로 쓰이는
_algebra는 거의 항상 -대수(학)으로 번역하면 무난. (다만 다른 것으로 번역될 수 있음, 아래 서술)

칼큘러스,calculus에서 어떤 _calculus 는 -대수(학)으로 번역되기도 함.
저기에는 정립된 번역이 없으며 -계산(법), -연산, -논리 등의 번역도 자주 보임.

Suffix -algebra:

수학의 분야명으로 쓰이는 suffix _algebra 중에서 어떤 것은 _logic , _calculus 와 완전히 구분되지 않음.
i.e.
앨지브라,algebra / 로직,logic / 칼큘러스,calculus의 경계선은 명확하지 않은 경우가 많음.

본질은 같은 것을 어떤 관점으로 / 어떤 방식으로 / .... 집중해서, 해석하는지 / 분석하는지 / 다루는지 ..... 에 따라 이름이 달라지는 듯
대체로 _algebra 는 대수적 관점, _logic 은 수리논리적 관점, _calculus 는 계산적 관점 ???

ex. 다음 것들은 비슷.

Boolean_algebra and Boolean_logic
// 불_대수,Boolean_algebra 불_논리,Boolean_logic ... curr at 불_식,Boolean_expression

propositional_logic and propositional_calculus
// 명제논리,propositional_logic

*th-order_calculus and *th-order_logic

...

그리고
logical_calculus Srch:logical_calculus
algebra_of_logic = logic_algebra = 논리대수 = Boolean_algebra[1]

Prefix algebraic- and algebraically-



ex.
Algebraic Propositional Logic
https://plato.stanford.edu/entries/logic-algebraic-propositional/
algebraic_propositional_logic

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4. 대수학 교재

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4.1. Serge Lang Algebra

Serge Lang
Serge_Lang
Algebra
Garduate Texts in Mathematics
Springer
두꺼운


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4.2. Weibel - Homological Algebra

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4.3. Hartshorne - Algebraic Geometry

Hartshorne - Algebraic Geometry
Ggl:Hartshorne Algebraic Geometry

Robin Hartshorne
Algebraic Geometry
Graduate Texts in Mathematics
Springer


algebraic_geometry 대수기하 대수기하학
KmsE:algebraic geom at @DATE
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5. 대수학 강의

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5.1. 오장헌

현대대수학1
세종대학교 오장헌
2015년 1학기
http://kocw.net/home/cview.do?cid=0d182cad13104050
평점 good
"The object of this course is to study the notion and theory of a 군,group.
One should be able to classify분류,classification groups of up to 오더,order 10.
Should be ablle to apply Sylow Theorems실로우_정리,쉴로브_정리,Sylow_theorem{ =,Sylow_theorem . Sylow_theorem Ndict:Sylow theorem WtEn:Sylow_theorem WpEn:Sylow_theorem -> https://en.wikipedia.org/wiki/Sylow_theorems https://ko.wikipedia.org/wiki/쉴로브_정리 ... Ggl:Sylow theorem / 실로우 via KmsE:sylow / 쉴로브 via 수백. } to solve various problems about groups.

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6. bmks ko

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앨지브라,algebra Modified on 4:02 pm, April 24, 2024.
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