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Ring (Notes) by Prof. M. Dabeer Mughal

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).

Name Ring (Notes) - Handwritten
Author Prof. M. Dabeer Mughal
Pages 64 pages
Format PDF & DjVu (see Software section for DjVu Reader
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 $\phi$ 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


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