مروری بر حدس اوسلَندر-رَیتن و برخی حدس‌های مرتبط با آن

[1] جعفری، امیر؛ یاسمی، سیامک، نظریهٔ رسته‌ها: هدف یا ابزار، فرهنگ و اندیشهٔ ریاضی، شماره ۷۱ (۱۴۰۱) ، ‎۴۷-۶۱‎.

[2] Araya, T., The Auslander-Reiten conjecture for Gorensetin rings, Proc. Amer. Ma.t.h.. .S.oc.., 137
(2009), 1941-1944.
[3] Assem, I., Simson, D., Skowro.ski, A., Elements of the Representation Theory of Associative Algebras,
Cambridge University Press, Cambridge, 2006.
[4] Auslander, M., Ding, S., Solberg, O., Liftings and weak liftings of modules, J. Algebra, 156 (1993),
273-317.

[5] Auslander, M., Reiten, I., On a generalized version of the Nakayam conjecture, Proc. Amer. Math.
Soc., 52 (1975), 69-74.
[6] Auslander, M., Reiten, I. Smalø, S. O., Representation Theory of Artin Algebras, Cambridge University
Press, Cambridge, 1995.
[7] Bass, H., Finitistic dimension and a homological generalization of semiprimary rings, Trans. Amer.
Math. Soc., 95 (1960), 466-488.
[8] Benson, D.J., Representations and Cohomology, vol. I., Cambridge University Press, Cambridge,
1991.
[9] Bruns, W., Herzog, J., Cohen-Macaulay Rings, Cambridge University Press, Cambridge, 1993.
[10] Enochs, E., Jenda, O. M. G., On Gorenstein injective modules, Comm. Algebra, 21 (1993), 3489-
3501.
[11] Enochs, E., Jenda, O. M. G., Gorensetin injective and projective modules, Math. Z., 220 (1995),
611-633.
[12] Enochs, E., Jenda, O. M. G., Relative Homological Algebra, De Gruyter, Berlin, 2000.
[13] Fomin, S., Zelevinsky, A., Cluster algebras, I. Foundation, J. Amer. Math. Soc., 15 (2002), 497-529.
[14] Happel, D., Triangulated Categories in the Representation Theory of Finite Dimensional Algebras,
Cambridge University Press, Cambridge, 1988.
[15] Happel, D., On Gorenstein algebras, in Representation Theory of Finite Groups and Finite Dimensional
Algebras, Birkhäuser Verlag, Basel, 1991, 389-404.
[16] Hartshorne, R., Residues and Duality, Springer-Verlag, Berlin, 1966.
[17] Hoshino, M., Modules wihout self-extensions and Nakayama’s conjecture, Arch. Math., 43 (1984),
494-500.
[18] Huisgen B. Z., Homological domino effects and the first finitistic dimension conjecture, Invent.
Math., 108 (1992), 369-383.
[19] Huneke, C., Leuschke, G. J., On a conjecture of Auslander and Reiten, J. Algebra, 275 (2004),
781-790.
[20] Jans, J. P., Some generalizations of finite projective dimension, Illinois J. Math., 5 (1961), 334-344.
[21] Kumashiro, S., The Auslander-Reiten conjecture for certain non-Gorensetin Cohen-Macaulay rings,
available at arXiv:2209.12718.
[22] Leuschke, G. J., Wiegand, R., Cohen-Macaulay Representations, Amer. Math. Soc., Providence,
Rhode Island, 2012.
[23] Mueller, B. J., The classification of algebras by dominant dimension, Canad. J. Math., 20 (1968),
398-409.
[24] Nakayama, T., On the complete cohomology theory of Frobenius algebras, Osaka Math. J., 9 (1957),
165-187.
[25] Nakayama, T., On algebras with complete homology, Abh. Math. Sem. Univ. Hamburg, 22 (1958),
300-307.
[26] Rotman, J. J., An Introduction to Homological Algebra, 2nd ed., Springer, Berlin, 2009.
[27] Sega, M., Vanishing of cohomology over Gorenstein rings of small codimension, Proc. Amer. Math.
Soc., 131 (2003), 2313-2323.
[28] Tachikawa, H., On dominant dimensions of QF-3 algebras, Trans. Amer. Math. Soc., 112 (1964),
249-266.
[29] Weibel, C. A., An Introduction to Homological Algebra, Cambridge University Press, Cambridge,
1994.