Ring (Notes) by Prof. M. Dabeer Mughal

Ring (Notes) 

by Prof. M. Dabeer Mughal

A written notes of Ring (Algebra) by faculty member. M.

Dabeer Mughal (Federal Directorate of Education, Islamabad, PAKISTAN).

Best to organize a “Rings & Vector Spaces” section of pure mathematics paper in SM (Mathematics).

Name	Ring (Notes) - Handwritten
Author	Prof. M. Dabeer Mughal
Pages	64 pages
Format	PDF
Size	PDF: 4.91MB, DjVu: 3.8MB

CONTENTS OR SUMMARY:

• Rings, commutative ring, ring with unity (identity), examples
• Consequences from the definition
• Unit element of ring
• Division ring or skew field, field, zero divisor
• Integral domain
• Characteristic of ring, Boolean ring
• Sub-ring and related theorem
• Centre of ring and related theorem
• Ring homomorphism
• Isomorphism, kernel of $\varphi$ and related theorems
• Ideal, left ideal
• Right ideal, two sided ideal, examples and theorems
• Principal ideal, principal ideal ring and related theorem
• Quotient ring and related theorem
• Ist fundamental theorem
• Maximal ideal and related theorem
• Prime ideal and related theorem
• The field of quotients of an integral domain
• Prime field

DOWNLOAD LINKS

• PDF File: Ring_Notes_Prof_M_Dabeer_Mughal.pdf ~ 4.91 MB

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Ring (Notes) Bs 7th Semester / MSC 2nd year

Ring (Notes) 

A written notes of Ring ( Abstract Algebra) by Professor. M. Dabeer Mughal (Federal Directorate of Education, Islamabad, PAKISTAN). Best to prepare a “Rings & Vector Spaces” section of Pure mathematics paper in MSC (Mathematics).

Name	Ring (Notes) - Handwritten
Author	Prof. M. Dabeer Mughal
Pages	64 pages
Format	PDF
Size	PDF: 4.95 MB

CONTENTS OR SUMMARY:

• Rings, commutative ring, ring with unity (identity), examples
• Consequences from the definition
• Unit element of ring
• Division ring or skew field, field, zero divisor
• Integral domain
• Characteristic of ring, Boolean ring
• Sub-ring and related theorem
• Centre of ring and related theorem
• Ring homomorphism
• Isomorphism, kernel of $\varphi$ and related theorems
• Ideal, left ideal
• Right ideal, two sided ideal, examples and theorems
• Principal ideal, principal ideal ring and related theorem
• Quotient ring and related theorem
• 1st fundamental theorem
• Maximal ideal and related theorem
• Prime ideal and related theorem
• The field of quotients of an integral domain
• Prime field

DOWNLOAD LINKS

• PDF File: Ring_Notes ~ 4.91 MB
  •  Link 1: Direct Link
  •  Link 2: mediafire.com

• Book : Abstract Algebra ~ 8.8 MB
  •  Link 1: Direct Link
  •  Link 2: mediafire.com

• To view online at Scribd [Click Here]
• To view online [Click Here]

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