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بنية جبرية (Info)


في الجبر التجريدي البنية الجبرية (بالإنجليزية: algebraic structure)‏ تتألف من مجموعة مزودة بمجموعة من العمليات أو العلاقات الرياضية المعرفة عليها بحيث تحقق بدهيات axiom معينة. مثلا الزمرة (G,*) يشار لها عادة بالزمرة G. في حال كانت المجموعة مزودة بعلاقات رياضية فقط دون أي عمليات نقول عنها أنها بنية علاقاتية relational structure.

قانون تركيب داخلي

تعريف

يرمز له عادة ب أو . نسمي عملية أو قانون تركيب داخلي كل تطبيق يربط عنصرين من نفس المجموعة بصورة ضمن تلك المجموعة بصفة عامة : ليكن و من مجموعة . قانون تركيب داخلي إذا كان :
حيث تسمى مجموعة مزودة بقانون تركيب داخلي ونكتب

خواص

التجميعية

القانون تجميعي تكافئ:

مثال:

التبادلية

القانون تبادلي تكافئ:

مثال:

العنصر المحايد

نقول ان عنصر محايد في بالنسبة ل إذا كان:

مثال : بالنسبة ل في المجموعة .

المماثل

مماثل في

يقبل عنصرا محايدا في
و

أمثلة لبعض البنيات الجبرية البسيطة

الزمرة

Source: wikipedia.org
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Algebraic Structures 1

Algebraic Structures 1

 
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Algebraic Structures - Groups

Algebraic Structures - Groups
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Algebraic Structures - Groups

Algebraic Structures - Groups
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Introduction To Algebraic Structures

Introduction To Algebraic Structures
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Basic Information In Algebraic Mathematics

Basic Information In Algebraic Mathematics
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Algebraic Equations

Algebraic Equations
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Introduction To Algebraic Structures

Introduction To Algebraic Structures
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Linear And Nonlinear Algebraic Systems

Linear And Nonlinear Algebraic Systems
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The Elements Of The Theory Of Algebraic Numbers

The Elements Of The Theory Of Algebraic Numbers
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The Elements Of The Theory Of Algebraic Numbers

The Elements Of The Theory Of Algebraic Numbers
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The Elements Of The Theory Of Algebraic Numbers

The Elements Of The Theory Of Algebraic Numbers
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Khayyam's Algebraic Letters

Khayyam's Algebraic Letters
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Plane Algebraic Curves

Plane Algebraic Curves
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Contemporary Mathematics Algebraic Structures

Contemporary Mathematics Algebraic Structures

 
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Public Domain
The Elements Of The Theory Of Algebraic Numbers

The Elements Of The Theory Of Algebraic Numbers
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Practical Applications In Algebraic Execution

Practical Applications In Algebraic Execution
Public Domain
Key To Davies' Bourdon : With Many Additional Examples, Illustrating The Algebraic Analysis : Also, A Solution Of All The Difficult Examples In Davies' Legendre

Key To Davies' Bourdon : With Many Additional Examples, Illustrating The Algebraic Analysis : Also, A Solution Of All The Difficult Examples In Davies' Legendre
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Arithmetic In Z - Algebraic Structures

Arithmetic In Z - Algebraic Structures
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An Essay On The Resolution Of Algebraic Equations

An Essay On The Resolution Of Algebraic Equations
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Ueber Riemann's Theorie Der Algebraischen Functionen

Ueber Riemann's Theorie Der Algebraischen Functionen
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An Essay On The Resolution Of Algebraic Equations

An Essay On The Resolution Of Algebraic Equations
Orientalists And Islamic Civilization - Irving And Islamic Algebra

Orientalists And Islamic Civilization - Irving And Islamic Algebra
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Public Domain
Geometric Exercises For Algebraic Solution; Second Year Mathematics For Secondary Schools

Geometric Exercises For Algebraic Solution; Second Year Mathematics For Secondary Schools
Women In Algebraic Literature

Women In Algebraic Literature

 
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Kindergarten Floral In Algebraic Assets.

Kindergarten Floral In Algebraic Assets.

 
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Chapter Two: Algebraic Expressions

Chapter Two: Algebraic Expressions
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A Modern Introduction To Algebraic Structures

A Modern Introduction To Algebraic Structures
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Examen des différentes méthodes employées pour résoudre les problèmes de géométrie. Paris, Vve Courcier, 1818

Examen des différentes méthodes employées pour résoudre les problèmes de géométrie. Paris, Vve Courcier, 1818
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"""fighting Killer"""
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Algebraic Analysis : Solutions And Exercises, Illustrating The Fundamental Theorems And The Most Important Processes Of Pure Algebra

Algebraic Analysis : Solutions And Exercises, Illustrating The Fundamental Theorems And The Most Important Processes Of Pure Algebra
Public Domain
Algebraic Geometry And Topology A Symposium In Honor Of S.lefschetz.

Algebraic Geometry And Topology A Symposium In Honor Of S.lefschetz.
4 Wonders Of Algebraic Antiquities

4 Wonders Of Algebraic Antiquities

 
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Differential Equations From The Algebraic Standpoint

Differential Equations From The Algebraic Standpoint
مناقشة ابن تيمية في حقيقة الجبرية

مناقشة ابن تيمية في حقيقة الجبرية
5 Wonders Of Algebraic Antiquities

5 Wonders Of Algebraic Antiquities

 
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الواضح في حكم الدولة الجبرية

الواضح في حكم الدولة الجبرية

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