Rings and Modules (2019)

Convener(s)

 
Name: Dinesh Khurana Ardeline Buhphang
Mailing Address: Panjab University, Chandigarh NEHU Shillong
Email:  dkhurana at pu.ac.in  ardeline17 at gmail.com

participants have to arrange for their own travel.

Dates: 

Monday, June 24, 2019 - 09:00 to Saturday, July 6, 2019 - 18:30

Venue: 

Venue Address: 

North-Eastern Hill University (NEHU), Umshing Mawkynroh, Shillong 793022, Meghalaya.

Venue State: 

Venue City: 

PIN: 

793022

Chrono Order: 

316

Syllabus: 

FIRST WEEK: Commutative Algebra

  • Day 1, Lecture 1: Commutative rings with unity, morphism of rings, ideals. Existence of maximal ideals.
    Prime ideals, nil radical. Polynomial rings.
  • Day 1, Lecture 2: Modules over commutative rings, morphism of modules, submodules, quotient modules,
    homomorphism theorems.
  • Day 2, Lecture 1: : Chinese remainder theorem, Division algorithm, Euclidean Domain, Principal Ideal
    Domain and Unique Factorization Domain.
  • Day 2, Lecture 2: : Product and coproduct of modules, free modules.
  • Day 3, Lecture 1: : Rings of fractions, extended and contracted ideals.
  • Day 3, Lecture 2: : Exact sequences of modules, commutative diagrams, four lemma, five lemma.
    Modules of fractions, local-global principles. Nakayama Lemma.
  • Day 4, Lecture 1: : Basics of Krull dimension of a ring. Integral extensions, weak Nullstellensatz.
  • Day 4, Lecture 2: : Dedekind domains, fractional ideals, class group.
  • Day 5, Lecture 1: : Noetherian rings and modules, Hilbert basis theorem.
  • Day 5, Lecture 2: : Modules over PIDs, Structure Theorem
  • Day 6, Lecture 1: : Affine algebras over a field, Hilbert Nullstellensatz, basics of affine algebraic varieties.
  • Day 6, Lecture 2: Lecture 2: Application of theory of finitely generated modules over PIDs to Linear
    Algebra.

 Text Books:
[1] M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Levant Books, Kolkata,2007.
[2] N. Jacobson, Basic Algebra-II, Second edition. W. H. Freeman and Company, New York, 1989.

SECOND WEEK: Non-Commutative Algebra

  • Day 1, Lecture 1: Basic differences between Commutative and Non-commutative rings, Examples of Non-commutative rings, One-sided ideals, Division rings, Simple rings, Ideals in matrix rings, Algebras.
  • Day 1, Lecture 2: Modules, Basic differences between vector spaces and modules, Chain conditions for modules and rings, One sided Artinian and Noetherian rings and failure of left-right symmetry, Modules of finite length, Composition series, Jordan Holder Theorem (statement only).
  • Day 2, Lecture 1: Semisimple Rings, Pierce Decompositions, Semisimple rings as direct products, Simple Artinian Rings.
  • Day 2, Lecture 2: Jacobson Radical, J-semisimple rings and their relationship with semisimple rings.
  • Day 3, Lecture 1: Jacobson’s Density Theorem, Schur’s Lemma, Wedderburn-Artin Theorem for Rings and Algebras.
  • Day 3, Lecture 2: Tensor Products of Modules and Algebras.
  • Day 4, Lecture 1: Bimodules, Finite dimensional algebras over fields, Central Simple Algebras.
  • Day 4, Lecture 2: Hom, Tensor Functors and their exactness.
  • Day 5, Lecture 1: Skolem-Noether Theorem, Double Centraliser Theorem, Splitting Field of Central Simple Algebras.
  • Day 5, Lecture 2: Projective, Injective and Flat Modules.
  • Day 6, Lecture 1: Wedderburn Theorem for finite division rings, Frobenius Theorem for division algebras over reals, Brauer Groups of fields.
  • Day 6, Lecture 2: Von-Neumann Rings as generalization of semisimple rings and their characterization as rings over which every module is flat.

Text Books:
[1] T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, 131. Springer-
Verlag, New York, 2001.
[2] T. Y. Lam, Lectures on modules and rings, Graduate Texts in Mathematics, 189. Springer-Verlag, New
York, 1999.

Speakers
1.Mrinal Kanti Das, ISI Kolkata
2.Utsav Choudhury, ISI Kolkata
3.Vikas Bist, Panjab University, Chandigarh
4.Dinesh Khurana, Panjab University, Chandigarh

Course Associates
1. Ardeline M. Buhphang, NEHU Shillong
2. Tikaram Subedi, NIT. Meghalaya.

Time Table: 

  9.30 - 11.00
Lecture 1		 11.30-1.00
Lecture 2		 2.30-3.30
Tutorial 1		 4.00-5.00
Tutorial 2
June 24 UC MKD UC, MKD, AMB UC, MKD, AMB
June 25 UC MKD MKD, UC, AMB MKD, UC, AMB
June 26 UC MKD UC, MKD, AMB UC, MKD, AMB
June 27 UC MKD MKD, UC, AMB MKD, UC, AMB
June 28 UC MKD UC, MKD, AMB UC, MKD, AMB
June 29 UC MKD MKD, UC, AMB MKD, UC, AMB
July 1 VB DK VB, DK, TS VB, DK, TS
July 2 VB DK DK, VB, TS DK, VB, TS
July 3 VB DK AKB, DK, TS VB, DK, TS
July 4 VB DK DK, VB, TS DK, VB, TS
July 5 VB DK AKB, DK, TS VB, DK, TS
July 6 VB DK DK, VB, TS DK, VB, TS

Tea Breaks: 11.00 - 11.30 and 3.30 - 4.00
Lunch Break: 1.00 - 2.30
Snacks: 5.00 - 5.30

 

Selected Applicants: 

Information for the participants:

Selected candidates are requested to confirm their participation by e-mailing the booked tickets to Professor Dinesh Khurana at dkhurana@pu.ac.in by April 30, 2019. The seats of the candidates who fail to do so will be offered to the candidates in the waiting list.

Accommodation is arranged in the Old Guest House, North-Eastern Hill University, Shillong. Breakfast and dinner will be served in the Guest House. Classes will be held in the Seminar Hall of Science Cluster Complex which is located on the second floor of the cluster complex. Lunch and tea will be arranged in the cluster complex itself. There are many canteens in the campus, a mall, two SBI ATM booths and some stationary shops. Participants will be allowed to access the central library by producing their badges. WiFi facility is available in both the Guest House and the Cluster Complex. Do not forget to carry an umbrella and some light sweaters, as it is rainy season and the temperature may drop down a bit in the morning and evening.

Sr. SID Full Name Gender Affiliation Univ/Inst.
M.Sc./M.A.		 Year of Passing M.Sc./M.A Ph.D. Deg. Date
1 23904 Mr. Surya Prakash Male CMP Degree College University of Allahabad University of Allahabad 2015  
2 23905 Mr. Ajim Uddin Ansari Male CMP Degree College University of Allahabad University of Allahabad 2015  
3 23908 Dr. Mohammad Salahuddin Khan Male Aligarh Muslim University Aligarh Muslim University 2007 03/12/2013
4 23953 Dr. Abdul Nadim Khan Male King Abdulaziz University MJP Rohilkhand University 2009 01/11/2014
5 23966 Dr. Avanish Kumar Chaturvedi Male University of Allahabad V B S P U Jaunpur 2003 25/07/2009
6 23984 Dr. Uday Shankar Chakraborty Male Assam University, Silchar Assam University, Silchar 2004 27/01/2010
7 24039 Mr. Abhyendra Prasad Male S R A P College Barachakia IIT Madras 2014  
8 24097 Dr. Dheerendra Mishra Male The LNM Institute of Information Technology, Jaipur Jiwaji University, Gwalior   03/04/2014
9 24126 Dr. Sarika Kushwaha Female Bhagalpur College Of Engineering University of Allahabad 2011 05/05/2018
10 24191 Dr. Manish Garg Male The LNM Institue of Information Technology, Jaipur Chaudhary Charan Singh University Uttar Pardesh 2007 27/07/2012
11 24226 Ms. Jane Roseline Yimchunger Female Kohima Science College North-Eastern Hill University 1999  
12 24227 Dr Aftab Hussain Shah Male Central University of Kashmir AMU Aligarh 2004 12/04/2010
13 24236 Dr. Aditya Mani Mishra Male Rajasthan Technical University Kota Motilal Nehru NIT Allahabad 2010 18/05/2014
14 24379 Prof. Suman Kalyan Ghosh Male Alliance University IIT Kanpur 2006  
15 24426 Mr. Sanjeev Kumar Maurya Male Adjunct Faculty, College of Engineering Pune VBS Purvanchal University, Jaunpur 2010  
16 24435 Dr. Krishnendu Das Male Netaji Subhas Mahavidyalaya University of Hyderabad 2009 14/08/2018
17 24655 Dr Sajad Hussain Ahangar Male Government Degree College Shopian University of Kashmir Srinagar 2007 27/06/2016
18 24905 Mr. Ajay Sharma Male Tezpur University Tezpur University 2015  
19 25535 Mr. Ravindra Kumar Male RSS Mahila College IIT Roorkee 2013  
20 25716 Mr Khwairakpam Herachandra Singh Male North Eastern Regional Institute of Science and Technology NEHU, Shillong 2003 15/03/2014
21 26117 Dr. Manoj Kumar Patel Male National Institute of Technology Nagaland VBS Poorvanchal University Jaunpur 2004 01/07/2011
22 26522 Dr. Paltu Sarkar Male University of North Bengal IIT KHARAGPUR 2008 05/12/2017
23 26853 Mr. Deepak Madhukar Bakal Male JSPM Jayawantrao Sawant College of Engineering University of Hyderabad 2018  
24 26911 Mr. Rahul Arora Male Malwa College S.C.D Government College 2008  
25 26978 Asst. Prof Soumen Pradhan Male Nagar College I.I.T. Kanpur 2012  
26 27053 Mr. Ranjan Sarkar Male Hijli college University of kalyani 2006  
27 27201 Mr. Sedevikho Chase Male Kohima Science College Dibrugarh University 2008  
28 27341 Mr. Debakanta Buragohain Male Tinsukia College Tezpur University 2009  
29 25891 Dr Gaurav Kumar Male GDC Hiranagar University of Jammu 2011 29/12/2017
30   Ashok Kumar          
Local Participants     
1 24411 Mr Laithun Boro Male NEHU MS 2017  
2 27342 Ms . Mridusmita Hazarika Female North Eastern Hill University north eastern hill university    
3 25814 Mr. Soumitra Das Male North-Eastern Hill University North-Eastern Hill University 2012  
4 26350 Mr. Ngangom Rojitkumar Singh Male NEHU MANIPUR UNIVERSITY 2012  
5 26244 Mr Kamakhya Paul Male NEHU PONDICHERRY UNIVERSITY 2015  
6 26251 Mr. Pravesh Sharma Male NEHU,Shillong NEHU 2016  
7 26559 Mr. Champak Talukdar Male NEHU Gauhati University 2017  
8 26728 Ms. Dimpy Mala Dutta Female North Eastern Hills University Tezpur University 2017  
9 26891 Mr. Snehashish Sarkar Male North eastern hill university Cotton university 2017  
10 26910 Mr Shanborlang Bynnud Male North Eastern Hills University North Eastern Hills University, Shillong 2016  
Waiting List     
1 27309 Ms Vitsono Lungalang Female Kohima Science College North Eastern Hill University 2003  
2 24606 Mr. Snehashis Mukherjee Male Ramakrishna mission Vivekananda educational and Research Institute University of calcutta 2018  
3 24672 Mr. Sushobhan Maity Male Visva-Bharati Visva-Bharati 2013  
4 26815 Ms. Shikha Patel Female Indian Institute of Technology Patna University of Allahabad 2016  
5 24056 Mr. Prajnan Kumar Bhagawati Male Gauhati University Pondicherry University 2017  
6 24180 Ms Padmapriya V P Female Central University of Kerala MG University, Kottayam 2014  
7 26341 Mr. Hariom . Male IIT DELHI IIT DELHI 2017  
8 27107 Mr. Sandeep Malik Male IIT Delhi IIT DELHI 2017  
9 27316 Ms. Dyuti Roy Female IISER-TIRUPATI VNIT Nagpur 2015  
10 26717 Mr. Sanjay Singha Male Indian Institute of Information Technology Vadodara VISVA-BHARATI 2018  
11 26440 Ms. Raneeta Dutta Female IISER Bhopal IIT Chennai 2016  
12 26265 Mr. Himangshu Hazarika Male Tezpur University Tezpur University 2018  
13 24964 Mr. Shiv Kumar Male IIT(B.H.U.) Varanasi M.J.P. Rohilkhand University Campus Bareilly (U.P.) 2014  
14 25261 Mr Bijon Biswas Male Jadavpur University University of Calcutta 2015  
15 26041 Mr. Nazim Khan Male Aligarh Muslim University Aligarh Muslim University 2015  
16 25700 Mr Ali Ahmed Abdullah Male Aligarh Muslim University Aligarh Muslim University 2015  
17 24012 Mr. Tushar Bag Male IIT Patna IIT Kanpur 2014  
18 26336 Mr. Priyadwip Das Male Jadavpur University Vidyasagar University 2015  

How to Reach: 

How to reach North-Eastern Hill University, Shillong.

From Guwahati Airport: One can take a shared tourist taxi from the airport to Police Bazar, Shillong, the cost is Rs. 500/- per person. From Police Bazar, one can directly hire a local cab upto NEHU Campus, the cost is about Rs. 200/-. Or one can go from Police Bazar to Polo Bazar and then take a shared taxi to the campus.

Alternately, one can get down at District Commissioner Office, near Wards Lake and take a university bus or a shared taxi from the point opposite to Raj Bhavan upto NEHU Campus.

From Guwahati Railway station: One can take a shared tourist taxi, the cost is Rs. 300/- per person or one can take a shared sumo or a bus upto Police Bazar and follow the same route as above.

From Shillong airport: There are local cabs available from Shillong airport upto Police Bazar, Shillong.

Contact Numbers for further assistance:

  1. Dr. A.M. Buhphang – (O) 0364-2722720, (M) 9436161409, (M) 8414033829.

  2. Mr. Soumitra Das – (M) 8974905463.

School Short Name: 

rm

Last Date Application: 

Sunday, March 31, 2019

School Type: 

IST