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General


This course is part of the MAGIC core.

Semester

Spring 2012 (Monday, January 16 to Friday, March 23)

Timetable
  • Wed 11:05 - 11:55
  • Fri 11:05 - 11:55

Lecturer


Moty Katzman
Email M.Katzman@sheffield.ac.uk
Phone (0114) 2223710
vcard
Photo of Moty Katzman


Students


Photo of Bana Al Subaiei
Bana Al Subaiei
(Southampton)
Photo of Badr Alharbi
Badr Alharbi
(East Anglia)
Photo of Robin Allan
Robin Allan
(Sheffield)
Photo of Hawazin Alzahrani
Hawazin Alzahrani
(Manchester)
Photo of Yumi Boote
Yumi Boote
(Manchester)
Photo of Tom Brookfield
Tom Brookfield
(Birmingham)
Photo of Yu-Yen Chien
Yu-Yen Chien
(Southampton)
Photo of Glen Collins
Glen Collins
(Birmingham)
Photo of Michael Cox
Michael Cox
(Birmingham)
Photo of Chris Draper
Chris Draper
(York)
Photo of Kostas Georgiadis
Kostas Georgiadis
(Loughborough)
Photo of Russell Goddard
Russell Goddard
(Nottingham)
Photo of Tom Harris
Tom Harris
(Southampton)
Photo of Heather Johnson
Heather Johnson
(Lancaster)
Photo of Andrew Jones
Andrew Jones
(Sheffield)
Photo of Alexandrou Maria
Alexandrou Maria
(Manchester)
Photo of Keith McCabe
Keith McCabe
(Durham)
Photo of David OSullivan
David OSullivan
(Sheffield)
Photo of Felix Rehren
Felix Rehren
(Birmingham)
Photo of Heather Riley
Heather Riley
(Liverpool)
Photo of Ilia Roustemoglou
Ilia Roustemoglou
(Loughborough)
Photo of David Ward
David Ward
(Manchester)
Photo of David Wilding
David Wilding
(Manchester)


Prerequisites


No prerequisites information is available yet.

Syllabus




Detailed Syllabus


Basic concepts: commutative rings, ideals, quotient rings, homomorphisms and algebras. (3 lecture)


Modules: homomorphisms, quotients and generating sets. (3 lecture)


Module finite extensions, Noether's Normalization Theorem and the weak form of Hilbert's Nullstellensatz. (4 lectures)


Localization. (3 lectures)


Noetherian rings and Hilbert's Basis Theorem. (3 lectures)


Primary decomposition of ideals. (1 lecture)


Algebraic sets: irreducible algebraic sets, the strong form of Hilbert's Nullstellensatz, and dimension (3 lectures)

Bibliography


Introduction to commutative algebra Atiyah and Macdonald
Steps in commutative algebra Sharp
Commutative algebra with a view toward algebraic geometry Eisenbud
Note:

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Assessment


No assessment information is available yet.

Assignments


Non -singular points

Files:Exam paper
Deadline: Friday 30 March 2012 (846.9 days ago)


Maximal chains of primes in polynomial rings

Files:Exam paper
Deadline: Friday 30 March 2012 (846.9 days ago)