Ring Notes Prof M Dabeer Mughal PDF

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Easy notes on ring theory...

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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

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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 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 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 Mughal

Federal Directorate of Education Islamabad, PAKISTAN

Available at http://www.MathCity.org/msc

BY:

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Prof. M. Dabeer Mughal Federal Directorate of Education Islamabad, PAKISTAN

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

Available at http://www.MathCity.org/msc

BY:

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

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

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...