Lectures On Unique Factorization Domains by Pierre Samuel
About this book :-
These lectures are a short, clear introduction to rings where every element can be broken down into “prime-like” building blocks in only one way (apart from ordering or harmless differences). It starts with basic ideas like the integer factorization and moves into more general scenarios like polynomial or power series rings. It showing how and when this unique breakdown happens. It also explains key theorems and gives helpful examples.
It cover some elementary properties of Krull rings and factorial rings, regular rings (local and factorial), and descent methods (Galoisian descent, the Purely inseparable case, formulae concerning derivations).
Book Detail :-
Title:
Lectures On Unique Factorization Domains by Pierre Samuel
Publisher:
Tata Institute Of Fundamental Research
Year:
1964
Pages:
17
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
Linked Content Owned by Author
Amazon:
Amazon
About Author :-
The author
Pierre Samuel
(1921 – 2009) was a French mathematician who worked in commutative algebra and its applications to algebraic geometry. The two-volume work Commutative Algebra that he wrote with Oscar Zariski is a classic. Other books of his covered projective geometry and algebraic number theory. Samuel studied at the Lycée Janson-de-Sailly in Paris before attending the École Normale Supérieure where he studied for his Agrégé de mathematique. He went to the United States to complete his research and was awarded a Master of Arts and then a Ph.D. from Princeton University in 1947 for his thesis "Ultrafilters and Compactification of Uniform Spaces". Returning to France, Samuel worked at the National Centre for Scientific research from 1947 to 1949. During this time he married Nicole Hermann on 23 July 1948; they had two children, Laurent and Fabien. In 1949 Samuel was appointed as Maître de Conférences at the Faculty of Science at Clermont-Ferrand and was later appointed as professor there. He continued to work there until 1961. Samuel ran a Paris seminar during the 1960s, and became Professeur émérite at the Université Paris-Sud (Orsay). His lectures on unique factorization domains published by the Tata Institute of Fundamental Research played a significant role in computing the Picard group of a Zariski surface via the work of Jeffrey Lang and collaborators. The method was inspired by earlier work of Nathan Jacobson and Pierre Cartier, another outstanding member of the Bourbaki group. Nicholas Katz related this to the concept of p-curvature of a connection introduced by Alexander Grothendieck. He was a member of the Bourbaki group, and filmed some of their meetings. A French television documentary on Bourbaki broadcast some of this footage in 2000.
Book Contents :-
1. Some preliminary results
2. Regular unique factorization domains
3. Power series over a UFD; reduction properties
4. Power series over a UFD. The two-dimensional case
5. Ground-field extensions
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