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.