# 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

### DOWNLOAD LINKS

**PDF File: Ring_Notes_Prof_M_Dabeer_Mughal.pdf ~ 4.91 MB**

**DjVu File: Ring_Notes_Prof_M_Dabeer_Mughal.djvu ~ 3.8 MB**

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

### Notes of other subjects

- Advanced Analysis: Handwritten Notes
- Algebra II by Syed Sheraz Asghar
- Complex Analysis (Easy Notes of Complex Analysis)
- Differential Geometry by Syed Hassan Waqas
- Differential Geometry: Handwritten Notes
- Fluid Mechanics I by Dr Rao Muzamal Hussain
- Functional Analysis by Mr. Tahir Hussain Jaffery
- Functional Analysis by Prof Mumtaz Ahmad
- Fundamental of Complex Analysis (Solutions of Some Exercises)
- General Topology by Raheel Ahmad
- Group Theory: Important Definitions and Results
- Groups (Handwritten notes)
- Linear Algebra: Important Definitions and Results
- Mathematical Method by Sir Muhammad Awais Aun
- Measure Theory Notes by Anwar Khan
- Mechanics (Easy Notes of Mechanics)
- Mechanics by Sir Nouman Siddique
- Metric Spaces (Notes)
- Number Theory by Dr Muhammad Umer Shuaib
- 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)

- msc/notes/ring_notes
- Last modified: 13 months ago
- by Administrator