Modules / Lectures

Module Name | Download | Description | Download Size |
---|---|---|---|

Ring theory basics | assignment1 | assignment1 | 87 kb |

Ring theory basics | assignment1-soln | assignment1-soln | 87 kb |

Ideals | assignment2 | assignment2 | 80 kb |

Ideals | assignment2-soln | assignment2-soln | 136 kb |

Module theory basics | assignment3 | assignment3 | 72 kb |

Module theory basics | assignment3-soln | assignment3-soln | 105 kb |

Homomorphism and Nakayama’s Lemma | assignment 4 | assignment 4 | 80 kb |

Homomorphism and Nakayama’s Lemma | assignment 4-solution | assignment 4-solution | 115 kb |

Properties of Modules | assignment5 | assignment5 | 78 kb |

Properties of Modules | assignment5-soln | assignment5-soln | 118 kb |

Localization | assignment6 | assignment6 | 85 kb |

Localization | assignment6-solution | assignment6-solution | 122 kb |

Localization and Integral dependence | assignment7 | assignment7 | 85 kb |

Localization and Integral dependence | assignment7-solution | assignment7-solution | 112 kb |

Going-up Theorem | assignment8 | assignment8 | 52 kb |

Going-up Theorem | assignment8-solution | assignment8-solution | 114 kb |

Going-down theorem and Chain conditions | assignment9 | assignment9 | 53 kb |

Going-down theorem and Chain conditions | assignment9-solution | assignment9-solution | 54 kb |

Properties of Noetherian rings | assignment10 | assignment10 | 70 kb |

Properties of Noetherian rings | assignment10-solution | assignment10-solution | 116 kb |

Primary decomposition and Artinian rings | assignment11 | assignment11 | 77 kb |

Primary decomposition and Artinian rings | assignment11-solution | assignment11-solution | 98 kb |

Noether Normalization and Hilbert’s Nullstellensatz | assignment12 | assignment12 | 76 kb |

Noether Normalization and Hilbert’s Nullstellensatz | assignment12-solution | assignment12-solution | 111 kb |

Sl.No | Chapter Name | English |
---|---|---|

1 | Review of Ring Theory | PDF unavailable |

2 | Review of Ring Theory (Ctd.) | PDF unavailable |

3 | Ideals in commutative rings | PDF unavailable |

4 | Operations on ideals | PDF unavailable |

5 | Properties of prime ideals | PDF unavailable |

6 | Colon and Radical of ideals | PDF unavailable |

7 | Radicals, extension and contraction of ideals | PDF unavailable |

8 | Modules and homomorphisms | PDF unavailable |

9 | Isomorphism theorems and Operations on modules | PDF unavailable |

10 | Operations on modules (Ctd.) | PDF unavailable |

11 | Module homomorphism and determinant trick | PDF unavailable |

12 | Nakayama’s lemma and exact sequences | PDF unavailable |

13 | Exact sequences (Ctd.) | PDF unavailable |

14 | Homomorphisms and Tensor products | PDF unavailable |

15 | Properties of tensor products | PDF unavailable |

16 | Properties of tensor products (Ctd.) | PDF unavailable |

17 | Tensor product of Algebras | PDF unavailable |

18 | Localization | PDF unavailable |

19 | Localization (Ctd.) | PDF unavailable |

20 | Local properties | PDF unavailable |

21 | Further properties of localization | PDF unavailable |

22 | Intergral dependence | PDF unavailable |

23 | Integral extensions | PDF unavailable |

24 | Lying over and Going-up theorems | PDF unavailable |

25 | Going-down theorem | PDF unavailable |

26 | Going-down theorem (Ctd.) | PDF unavailable |

27 | Chain conditions | PDF unavailable |

28 | Noetherian and Artinian modules | PDF unavailable |

29 | Properties of Noetherian and Artinian modules, Composition Series | PDF unavailable |

30 | Further properties of Noetherian and Artinian modules and rings | PDF unavailable |

31 | Hilbert basis theorem and Primary decomposition | PDF unavailable |

32 | Primary decomposition (Ctd.) | PDF unavailable |

33 | Uniqueness of primary decomposition | PDF unavailable |

34 | 2nd Uniqueness theorem, Artinian rings | PDF unavailable |

35 | Properties of Artinian rings | PDF unavailable |

36 | Structure Theorem of Artinian rings | PDF unavailable |

37 | Noether Normalization | PDF unavailable |

38 | Hilberts Nullstellensatz | PDF unavailable |

Sl.No | Language | Book link |
---|---|---|

1 | English | Not Available |

2 | Bengali | Not Available |

3 | Gujarati | Not Available |

4 | Hindi | Not Available |

5 | Kannada | Not Available |

6 | Malayalam | Not Available |

7 | Marathi | Not Available |

8 | Tamil | Not Available |

9 | Telugu | Not Available |