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# Ring (Notes) by Prof. M. Dabeer Mughal

A handwritten notes on Ring (Algebra) by Prof. M. Dabeer Mughal (Federal Directorate of Education, Islamabad, Pakistan). It is best to prepare a “Rings and Vector Spaces” section of your algebra paper or Algebra II for BS or MS Mathematics.

Name | Ring (Notes) - Handwritten |
---|---|

Author | Prof. M. Dabeer Mughal |

Pages | 64 pages |

Format | PDF & DJVU (see Software section for viewers) |

Size | PDF: 4.90MB 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