ring (notes) by prof m dabeer mughal
DESCRIPTION
A handwritten notes of Ring (Algebra) by Prof. M. Dabeer Mughal (Federal Directorate of Education, Islamabad, PAKISTAN). Best to prepare a “Rings & Vector Spaces” section of Algebra paper in MSc (Mathematics).TRANSCRIPT
Ring (Notes)
by
Prof. M. Dabeer Mughal
Federal Directorate of Education
Islamabad, PAKISTAN
Partial Contents
1. Rings, commutative ring, ring with unity (identity), examples 1
2. Consequences from the definition 3
3. Unit element of ring 4
4. Division ring or skew field, field, zero divisor 5
5. Integral domain 7
6. Characteristic of ring, Boolean ring 8
7. Sub-ring and related theorem 9
8. Centre of ring and related theorem 11
9. Ring homomorphism 16
10. Isomorphism, kernel of φ and related theorems 17
11. Ideal, left ideal 20
12. Right ideal, two sided ideal, examples and theorems 21
13. Principal ideal, principal ideal ring and related theorem 28
14. Quotient ring and related theorem 37
15. Ist fundamental theorem 42
16. Maximal ideal and related theorem 44
17. Prime ideal and related theorem 49
18. The field of quotients of an integral domain 52
19. Prime field 63
Available at http://www.MathCity.org/mscWe are very thankful to Prof. M. Dabeer Mughal for sharing these notes.
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Dated: September 15, 2010
Ring (Notes)
Available at http://www.MathCity.org/msc
Prof. M. Dabeer Mughal
Federal Directorate of Education
Islamabad, PAKISTAN
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Prof. M. Dabeer MughalFederal Directorate of Education
Islamabad, PAKISTAN
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Prof. M. Dabeer MughalFederal Directorate of EducationIslamabad, PAKISTAN
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Prof. M. Dabeer MughalFederal Directorate of Education
Islamabad, PAKISTAN
Available at http://www.MathCity.org/msc
Prof. M. Dabeer Mughal
Federal Directorate of Education
Islamabad, PAKISTANBY:{
Available at http://www.MathCity.org/msc
Prof. M. Dabeer Mughal
Federal Directorate of EducationIslamabad, PAKISTAN
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Prof. M. Dabeer Mughal
Federal Directorate of Education
Islamabad, PAKISTANBY:
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Prof. M. Dabeer MughalFederal Directorate of Education
Islamabad, PAKISTAN
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Prof.
M.
Dabeer
Mughal
Federal
Directorate
ofEducation
Islamabad,PAKISTAN
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc
Available at http://www.MathCity.org/msc