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@article{FPM_2009_15_8_a2, author = {P. A. Krylov and A. A. Tuganbaev}, title = {Modules over formal matrix rings}, journal = {Fundamentalʹna\^a i prikladna\^a matematika}, pages = {145--211}, publisher = {mathdoc}, volume = {15}, number = {8}, year = {2009}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_8_a2/} }
P. A. Krylov; A. A. Tuganbaev. Modules over formal matrix rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 8, pp. 145-211. http://geodesic.mathdoc.fr/item/FPM_2009_15_8_a2/
[1] Kashu A. I., “O lokalizatsiyakh v Morita-kontekstakh”, Mat. sb., 133(175):1 (1987), 127–133 | Zbl
[2] Krylov P. A., “Ob izomorfizme kolets obobschënnykh matrits”, Algebra i logika, 47:4 (2008), 456–463 | MR | Zbl
[3] Krylov P. A., Yardykov E. Yu., “O proektivnykh i nasledstvennykh modulyakh nad koltsami obobschënnykh matrits”, Fundament. i prikl. mat., 14:5 (2008), 125–138 | MR
[4] Feis K., Algebra: koltsa, moduli i kategorii, v. 1, Mir, M., 1977
[5] Fuks L., Beskonechnye abelevy gruppy, v. 1, Mir, M., 1974
[6] Yardykov E. Yu., “Prostye moduli nad koltsami obobschënnykh matrits”, Fundament. i prikl. mat., 13:3 (2007), 245–247 | MR | Zbl
[7] Abujabal H. A. S., Nauman S. K., “A construction of Morita similar endomorphism rings”, J. Algebra, 235 (2001), 453–458 | DOI | MR | Zbl
[8] Anderson F. W., Fuller K. R., Rings and Categories of Modules, Springer, New York, 1974 | MR | Zbl
[9] Asadollahi J., Salarian S., “On the vanishing of Ext over formal triangular matrix rings”, Forum Math., 18:6 (2006), 951–966 | DOI | MR | Zbl
[10] Auslander M., Reiten I., Smalø S. O., Representation Theory of Artin Algebras, Cambridge Univ. Press, Cambridge, 1995 | MR | Zbl
[11] Birkenmeier G. F, Park J. K., Rizvi S. T., “Generalized triangular matrix rings and the fully invariant extending property”, Rocky Mountain J. Math., 32:4 (2002), 1299–1319 | DOI | MR | Zbl
[12] Company Cabezos M., Gomez Lozano M., Siles Molina M., “Exchange Morita rings”, Commun. Algebra, 29:2 (2001), 907–925 | DOI | MR | Zbl
[13] Chen H., “Stable ranges for Morita contexts”, Southeast Asian Math. Bull., 25 (2001), 209–216 | DOI | MR | Zbl
[14] Chen H., “Morita contexts with many units”, Commun. Algebra, 30:3 (2002), 1499–1512 | DOI | MR | Zbl
[15] Chen H., “Strongly $\pi$-regular Morita contexts”, Bull. Korean Math. Soc., 40:1 (2003), 91–99 | DOI | MR | Zbl
[16] Chen H., “Ideals in Morita rings and Morita semigroups”, Acta Math. Sinica, 21:4 (2005), 893–898 | DOI | MR | Zbl
[17] Fossum R. M, Griffith P. A., Reiten I., Trivial Extensions of Abelian Categories, Lect. Notes Math., 456, Springer, Berlin, 1975 | MR | Zbl
[18] Ghahramani H., Moussavi A., “Differential polynomial rings of triangular matrix rings”, Bull. Iranian Math. Soc., 34:2 (2008), 71–96 | MR | Zbl
[19] Goodearl K. R., Ring Theory, Marcel Dekker, New York, 1976 | MR | Zbl
[20] Green E. L., “On the representation theory of rings in matrix form”, Pacific J. Math., 100:1 (1982), 123–138 | DOI | MR | Zbl
[21] Haghany A., “Morita contexts and torsion theories”, Math. Japon., 42:1 (1995), 137–142 | MR | Zbl
[22] Haghany A., “On the torsion theories of Morita equivalent rings”, Period. Math. Hungar., 32 (1996), 193–197 | DOI | MR | Zbl
[23] Haghany A., “Hopficity and co-hopficity for Morita contexts”, Commun. Algebra, 27:1 (1999), 477–492 | DOI | MR | Zbl
[24] Haghany A., “Injectivity conditions over a formal triangular matrix ring”, Arch. Math., 78 (2002), 268–274 | DOI | MR | Zbl
[25] Haghany A., Varadarajan K., “Study of formal triangular matrix rings”, Commun. Algebra, 27:11 (1999), 5507–5525 | DOI | MR | Zbl
[26] Haghany A., Varadarajan K., “Study of modules over formal triangular matrix rings”, J. Pure Appl. Algebra, 147:1 (2000), 41–58 | DOI | MR | Zbl
[27] Haghany A., Varadarajan K., “IBN and related properties for rings”, Acta Math. Hungar., 94:3 (2002), 251–261 | DOI | MR | Zbl
[28] Harada M., “On semiprimary PP-rings”, Osaka J. Math., 2 (1965), 153–161 | MR | Zbl
[29] Herstein I. N., “A counter-example in Noetherian rings”, Proc. Nat. Acad. Sci. U.S.A., 54 (1965), 1036–1037 | DOI | MR | Zbl
[30] Hirano Y., “Another triangular matrix ring having Auslander–Gorenstein property”, Commun. Algebra, 29 (2001), 719–735 | DOI | MR | Zbl
[31] Iwanaga Y., Wakamatsu T., “Auslander–Gorenstein property of triangular matrix rings”, Commun. Algebra, 23:10 (1995), 3601–3614 | DOI | MR | Zbl
[32] Khazal R., Dascalescu S., van Wyk L., “Isomorphism of generalized triangular matrix rings and recovery of tiles”, Int. J. Math. Math. Sci., 2003:9 (2003), 533–538 | DOI | MR | Zbl
[33] Krylov P. A., Mikhalev A. V., Tuganbaev A. A., Endomorphism Rings of Abelian Groups, Kluwer Academic, Dordrecht, 2003 | MR | Zbl
[34] Krylov P. A., Tuganbaev A. A., Modules over Discrete Valuation Domains, De Gruyter Exp. Math., 43, Walter de Gruyter, Berlin, 2008 | DOI | Zbl
[35] Lam T. Y., Lectures on Rings and Modules, Springer, New York, 1999 | MR
[36] Loustaunau P., Shapiro J., “Homological dimensions in a Morita context with applications to subidealizers and fixed rings”, Proc. Amer. Math. Soc., 110:3 (1990), 601–610 | DOI | MR | Zbl
[37] Loustaunau P., Shapiro J., “Morita contexts”, Non-Commutative Ring Theory, Proc. Conf. (Athens/OH, USA, 1989), Lect. Notes Math., 1448, Springer, Berlin, 1990, 80–92 | DOI | MR
[38] Loustaunau P., Shapiro J., “Localization in Morita context with applications to fixed rings”, J. Algebra, 143 (1991), 373–387 | DOI | MR | Zbl
[39] Marubayashi H., Zhang Y., Yang P., “On the rings of Morita context which are some well-known orders”, Commun. Algebra, 26:5 (1998), 1429–1444 | DOI | MR | Zbl
[40] Maxson C. J., “Near-rings of homogeneous functions”, Nearrings, Nearfields and $K$-Loops, Proc. of the Conf. on Nearrings and Nearfields (Hamburg, Germany, July 30 – August 2, 1995), Math. Appl., 426, eds. G. Saad et al., Kluwer Academic, Dordrecht, 1997, 35–46 | MR | Zbl
[41] Ming K., “On FI-extending modules”, J. Chungcheong Math. Soc., 16:2 (2003), 79–88 | MR
[42] Morita K., “Duality for modules and its applications to the theory of rings with minimum condition”, Sci. Rep. Tokyo Kyoiku Daigaku, 6 (1958), 83–142 | MR | Zbl
[43] Müller B. J., “The quotient category of a Morita context”, J. Algebra, 28 (1974), 389–407 | DOI | MR | Zbl
[44] Müller M., “Rings of quotients of generalized matrix rings”, Commun. Algebra, 15 (1987), 1991–2015 | DOI | MR | Zbl
[45] Nauman S. K., “Morita similar matrix rings and their Grothendieck groups”, Aligarh Bull. Math., 23:1–2 (2004), 49–60 | MR
[46] Palmer I., “The global homological dimension of semi-trivial extensions of rings”, Math. Scand., 37 (1975), 223–256 | MR
[47] Palmer I., Roos J. E., “Explicit formulae for the global homological dimension of trivial extensions of rings”, J. Algebra, 27 (1974), 380–413 | DOI | MR
[48] Poole D. G., Stewart P. N., “Classical quotient rings of generalized matrix rings”, Int. J. Math. Math. Sci., 18:2 (1995), 311–316 | DOI | MR | Zbl
[49] Sakano K., “Maximal quotient rings of generalized matrix rings”, Commun. Algebra, 12:16 (1984), 2055–2065 | DOI | MR | Zbl
[50] Sands A. D., “Radicals and Morita contexts”, J. Algebra, 24 (1973), 335–345 | DOI | MR | Zbl
[51] Sheiham D., “Universal localization of triangular matrix rings”, Proc. Amer. Math. Soc., 134:2 (2006), 3465–3474 | DOI | MR | Zbl
[52] Small I. N., “An example in Noetherian rings”, Proc. Nat. Acad. Sci. U.S.A., 54 (1965), 1035–1036 | DOI | MR | Zbl
[53] Veldsman S., “Radicals of Morita rings revisited”, Bul. Acad. Şti. Rep. Moldova Mat., 2007, no. 2, 55–68 | MR | Zbl
[54] Zhou Zh., “Semisimple quotient rings and Morita context”, Commun. Algebra, 21:7 (1993), 2205–2210 | DOI | MR | Zbl