Università di Pavia - Offerta formativa
Language: it en
COMPLEMENTS OF ALGEBRA
Stampa
Enrollment year
2020/2021
Academic year
2020/2021
Regulations
DM270
Academic discipline
MAT/02 (ALGEBRA)
Department
DEPARTMENT OF MATHEMATICS "FELICE CASORATI"
Course
MATHEMATICS
Curriculum
PERCORSO COMUNE
Year of study
1°
Period
1st semester (01/10/2020 - 20/01/2021)
ECTS
6
Lesson hours
48 lesson hours
Language
Italian
Activity type
ORAL TEST
Teacher
CANONACO ALBERTO (titolare) - 6 ECTS
Prerequisites
The contents of the courses: Linear Algebra, Algebra 1 and Algebra 2.
Learning outcomes
The aim of the course is to provide an introduction to noncommutative algebra.
Course contents
Example of noncommutative rings. (Left or right) modules over a ring and bimodules. Artinian and Noetherian rings and modules. Semisimple rings and modules; Wedderburn-Artin theorem. Jacobson radical and J-semisimple rings. Local rings and Krull-Schmidt theorem; semilocal rings. Further possible topics include: (semi)prime rings and primitive rings; (semi)perfect rings and homological properties; module categories and Morita theory; simple rings and Brauer group of a field.
Teaching methods
Lectures
Reccomended or required readings
P. Aluffi, "Algebra: chapter 0", Graduate Studies in Mathematics 104, American Mathematical Society, 2009.
T.Y. Lam, "A first course in noncommutative rings", second edition, Graduate Texts in Mathematics 131, Springer-Verlag, 2001.
T.Y. Lam, "Lectures on rings and modules", Graduate Texts in Mathematics 189, Springer-Verlag, 1998.
R.S. Pierce, "Associative algebras", Graduate Texts in Mathematics 88, Springer-Verlag, 1982.
Assessment methods
The exam consists of an oral examination, during which the student must answer some questions, mainly of a theoretical nature.
Further information
Sustainable development goals - Agenda 2030

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