Ring (Notes) 

by Prof. M. Dabeer Mughal

Notes by Prof. M. Dabeer Mughal

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).
NameRing (Notes) - Handwritten
AuthorProf. M. Dabeer Mughal
Pages64 pages
SizePDF: 4.91MB, DjVu: 3.8MB


  • Rings, commutative ringring 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 ϕ 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

  • PDF File: Ring_Notes_Prof_M_Dabeer_Mughal.pdf ~ 4.91 MB

Notes of other subjects

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  • Differential Geometry: Handwritten Notes
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  • Fundamental of Complex Analysis (Solutions of Some Exercises)
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  • Number Theory: Handwritten Notes
  • Number Theory: Notes by Anwar Khan
  • Numerical Analysis by M Usman Hamid
  • Numerical Analysis II
  • Operation Research by Sir Haidar Ali
  • Operation Research: Handwritten Notes
  • Real Analysis (Notes by Prof. Syed Gul Shah)
  • Ring (Notes) by Prof. M. Dabeer Mughal
  • Rings (Handwritten notes)
  • Theory of Relativity & Analytic Dynamics: Handwritten Notes
  • Topology Notes by Azhar Hussain
  • Topology: Handwritten Notes
  • Vector Spaces (Handwritten notes)

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