Direct summands of direct sums of modules whose endomorphism rings have two maximal right ideals
Tài liệu tham khảo
Amini, 2008, Equivalence of diagonal matrices over local rings, J. Algebra, 320, 1288, 10.1016/j.jalgebra.2008.04.008
Anderson, 1992
Cohn, 1977, vol. 27
Diracca, 2002, Uniqueness of monogeny classes for uniform objects in abelian categories, J. Pure Appl. Algebra, 172, 183, 10.1016/S0022-4049(01)00160-8
Dung, 1998, Direct summand of serial modules, J. Pure Appl. Algebra, 133, 93, 10.1016/S0022-4049(97)00186-2
Facchini, 1996, Krull–Schmidt fails for serial modules, Trans. Amer. Math. Soc., 348, 4561, 10.1090/S0002-9947-96-01740-0
Facchini, 1998, vol. 167
Facchini, 2007, Representations of additive categories and direct-sum decompositions of objects, Indiana Univ. Math. J., 56, 659, 10.1512/iumj.2007.56.2865
Facchini, 2008, Injective modules, spectral categories, and applications, vol. 456, 1
Facchini, 2000, Projective modules over semilocal rings, vol. 259, 181
Facchini, 2006, Local morphisms and modules with a semilocal endomorphism ring, Algebr. Represent. Theory, 9, 403, 10.1007/s10468-006-9011-8
A. Facchini, P. Příhoda, Endomorphism rings with finitely many maximal right ideals, Comm. Algebra (2010) (in press).
A. Facchini, P. Příhoda, The Krull–Schmidt theorem in the case two, Algebr. Represent. Theory (2010) (in press). Online first doi:10.1007/s10468-009-9202-1 2009.
Facchini, 2004, Direct-sum decompositions of modules with semilocal endomorphism ring, J. Algebra, 274, 689, 10.1016/j.jalgebra.2003.06.004
Gabriel, 1966, Spektralkategorien und reguläre Ringe im Von-Neumannschen Sinn, Math. Z., 82, 389, 10.1007/BF01112218
Mac Lane, 1997
Mitchell, 1972, Rings with several objects, Adv. Math., 8, 1, 10.1016/0001-8708(72)90002-3
Příhoda, 2004, Weak Krull–Schmidt theorem and direct sum decompositions of serial modules of finite Goldie dimension, J. Algebra, 281, 332, 10.1016/j.jalgebra.2004.06.027