Předmět je zakončen ústní zkouškou.

(1) M. Auslander, Isolated singularities and existence of almost split sequences, in: Representation

Theory, II, Ottawa, Ont., 1984, in: Lecture Notes in Math., vol. 1178, Springer, Berlin, 1986.

(2) ] M. Auslander, Representation theory of Artin algebras II, Comm. Algebra 1 (1974) 269-310.

(3) M. Auslander, Relations for Grothendieck groups of Artin algebras, Proc. Amer. Math. Soc. 91

(3)(1984) 336-340.

(4) M. Auslander, I. Reiten, Grothendieck groups of algebras and orders, J. Pure Appl. Algebra 39

(1-2) (1986) 1-51.

(5) Y. Yoshino, Cohen-Macaulay Modules over Cohen-Macaulay Rings, London Mathematical Society Lecture Note Series, vol. 146, Cambridge University Press, Cambridge, 1990.

(6) T. Kobayashi, Syzygies of Cohen-Macaulay modules and Grothendieck groups, J. Algebra 490

(2017) 372-379.

(7) H. Enomoto; Classifications of exact structures and Cohen-Macaulay-finite algebras, Advances

in Mathematics Volume 335, 7 September 2018, Pages 838-877.

(8) H. Enomoto; Relations for Grothendieck groups and representation-finiteness; Journal of Algebra

Volume 539, 1 December 2019, Pages 152-176.

(1) M. Auslander, Isolated singularities and existence of almost split sequences, in: Representation

Theory, II, Ottawa, Ont., 1984, in: Lecture Notes in Math., vol. 1178, Springer, Berlin, 1986.

(2) ] M. Auslander, Representation theory of Artin algebras II, Comm. Algebra 1 (1974) 269-310.

(3) M. Auslander, Relations for Grothendieck groups of Artin algebras, Proc. Amer. Math. Soc. 91

(3)(1984) 336-340.

(4) M. Auslander, I. Reiten, Grothendieck groups of algebras and orders, J. Pure Appl. Algebra 39

(1-2) (1986) 1-51.

(5) Y. Yoshino, Cohen-Macaulay Modules over Cohen-Macaulay Rings, London Mathematical Society Lecture Note Series, vol. 146, Cambridge University Press, Cambridge, 1990.

(6) T. Kobayashi, Syzygies of Cohen-Macaulay modules and Grothendieck groups, J. Algebra 490

(2017) 372-379.

(7) H. Enomoto; Classifications of exact structures and Cohen-Macaulay-finite algebras, Advances

in Mathematics Volume 335, 7 September 2018, Pages 838-877.

(8) H. Enomoto; Relations for Grothendieck groups and representation-finiteness; Journal of Algebra

Volume 539, 1 December 2019, Pages 152-176.

The course is completed with an oral exam. The requirements for the exam correspond to what is presented in lectures.

Předmět je zakončen ústní zkouškou. Požadavky u zkoušky budou odpovídat rozsahu, ve kterém bylo téma prezentováno na přednášce.

This course will be about Cohen-Macaulay modules over local Cohen-Macaulay rings, with a view

towards Auslander-Reiten sequences and what it means for such sequences to generate the relations of

the Grothendieck group. Depending on time and interest, we may consider these questions in the

generality of Exact categories which has applications to (Cohen-Macaulay) orders.

(1) Recalling definitions of Cohen-Macaulay rings, (maximal)Cohen-Macaulay modules, Gorenstein

rings.

(2) Exact categories.

(3) Auslander-Reiten sequences.

(4) Functor categories, and the subcategories of finitely generated, and finitely presented functors.

(5) Grothendieck groups.

(6) When are the relations in the Grothendieck group generated by Auslander-Reiten sequences ?

This course will be about Cohen-Macaulay modules over local Cohen-Macaulay rings, with a view

towards Auslander-Reiten sequences and what it means for such sequences to generate the relations of

the Grothendieck group. Depending on time and interest, we may consider these questions in the

generality of Exact categories which has applications to (Cohen-Macaulay) orders.

(1) Recalling definitions of Cohen-Macaulay rings, (maximal)Cohen-Macaulay modules, Gorenstein

rings.

(2) Exact categories.

(3) Auslander-Reiten sequences.

(4) Functor categories, and the subcategories of finitely generated, and finitely presented functors.

(5) Grothendieck groups.

(6) When are the relations in the Grothendieck group generated by Auslander-Reiten sequences?