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    Ring (Notes) by Prof M Dabeer Mughal

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    atiq4pk
    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).

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    Download as PDF, TXT or read online from Scribd

    Ring (Notes) by Prof M Dabeer Mughal

    Uploaded by

    atiq4pk
    6K views64 pages
    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).

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    © Attribution Non-Commercial (BY-NC)

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    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).

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    6K views64 pages

    Ring (Notes) by Prof M Dabeer Mughal

    Uploaded by

    atiq4pk
    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).

    Copyright:

    Attribution Non-Commercial (BY-NC)
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 64
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    The notes cover various topics related to rings including definitions, properties, examples, theorems related to subrings, ideals, homomorphisms and fields.

    The notes cover topics like commutative rings, units, zero divisors, integral domains, characteristics of rings, subrings, ideals, homomorphisms, fields of quotients.

    The notes were written by Prof. M. Dabeer Mughal of the Federal Directorate of Education in Islamabad, Pakistan.

    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/msc
    We are very thankful to Prof. M. Dabeer Mughal for sharing these notes.

    MathCity.org is a non-profit organization, working to promote mathematics in Pakistan. If


    you have anything (notes, model paper, old paper etc.) to share with other peoples, you can
    send us to publish on MathCity.org.
    For more information visit: http://www.MathCity.org/participate

    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
    {
    Prof. M. Dabeer Mughal
    BY: 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
    Prof. M. Dabeer Mughal
    BY: 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

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