USTC Algebra Notes


The following is a series of informal notes, where no originality is claimed. We collect them into the so-called USTC Algebra Notes. The PDF files of the notes are freely available online, while the copyright are held by the authors. Please contact Xiao-Wu Chen if you intend to put a note in this series, or if you have comments and corrections to these notes.



1. Two lemmas on the axiom (TR4), No. 1, Feb. 2014.


2. The torsion subgroup of an abelian group, No. 2, Mar. 2015.


3. A note on torsion pairs, No. 3, Jan. 2017.


4. Adjoint pairs and canonical morphisms for bimodules, No. 4, May 2018.


5. Double complexes and total complexes, No. 5, June 2018.


6. The Extension-Lifting Lemma via two-term complexes, No. 6, Nov. 2018.


7. The Auslander algebra of truncated polynomial algebra, No. 7, Oct. 2019.


8. The radical vectors of Cartan matrices, No. 8, Nov. 2019.


9. The 2-Calabi-Yau completion via Auslander-Reiten theory, No. 9, Sept. 2021.


10. The signs in the bar resolution, No. 10, Oct. 2021.


11. On trivial extensions of monomial algebras, No. 11, Nov. 2021.


12. On weak idempotent completions, May 6, 2024.