# Rings & Modules by Ms. Iqra Liaqat

These notes are send by Ms. iqra-liaqat. We are really very thankful to her for providing these notes and appreciates her effort to publish these notes on MathCity.org

Name | Rings & Modules |
---|---|

Author | Ms. Iqra Liaqat |

Pages | 140 pages |

Format | PDF (see Software section for PDF Reader) |

Size | 5.88 mB |

### Contents & Summary

- Groupoid
- Semi group
- Group
- Subgroup
- Ring
- Field
- Vector space
- Module
- Unital R module
- Module homomorphism
- Monomorphism
- Epimorphism
- Isomorphism
- Kernal of homomorphism
- Range of T
- Ring homomorphism
- Quotient Module
- First theorem of homomorphism
- Second isomorphism theorem
- Fundamental theorem of homomorphism
- Internal direct sum
- External direct sum
- Finitely generated module
- Cyclic module
- Torsion free module

- Torsion element
- Freely generated module
- Linearly independent & dependent set
- Polynomial ring
- Degree of polynomial
- Constant polynomial
- Remainder theorem
- Zeros of the polynomial
- Roots of the equation
- Factor theorem
- Existence theorem
- Gaussian integer and ring of Gaussian integer
- Prime
- Irreducible element
- Irreducible polynomial over field
- Monic polynomial
- Unique factorization domain (U.F.O)
- Principle ideal
- Principle ideal domain
- Euclidean domain
- Factorization domain

### Download

### Notes of other subjects

- Advance Analysis by Ms. Iqra Liaqat
- Advanced Analysis: Handwritten Notes
- Algebra II by Syed Sheraz Asghar
- Complex Analysis (Easy Notes of Complex Analysis)
- Complex Analysis (Quick Review)
- Differential Geometry by M Usman Hamid
- Differential Geometry by Syed Hassan Waqas
- Differential Geometry: Handwritten Notes
- Fluid Mechanics I by Dr Rao Muzamal Hussain
- Fluid Mechanics II 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 by Mr. Muhammad Iftikhar
- Group Theory: Important Definitions and Results
- Groups (Handwritten notes)
- Linear Algebra: Important Definitions and Results
- Mathematical Method by Sir Muhammad Awais Aun
- Mathematical Statistics I by Muzammil Tanveer
- Mathematical Statistics II by Sir Haidar Ali
- 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
- Partial Differential Equations
- Partial Differential Equations by M Usman Hamid
- Real Analysis (Notes by Prof. Syed Gul Shah)
- Ring (Notes) by Prof. M. Dabeer Mughal
- Rings & Modules by Ms. Iqra Liaqat
- Rings (Handwritten notes)
- Special Functions by Dr. Muhey-U-Din
- Theory of Optimization by Ma'am Iqra Razzaq
- Theory of Relativity & Analytic Dynamics: Handwritten Notes
- Topology Notes by Azhar Hussain
- Topology: Handwritten Notes
- Vector Spaces (Handwritten notes)

- msc/notes/rings-and-modules-iqra-liaqat
- Last modified: 7 weeks ago
- by Dr. Atiq ur Rehman