Amini, Afshin; Amini, Babak; Facchini, Alberto
Weak Krull-Schmidt for Infinite Direct Sums of Cyclically Presented Modules over Local Rings
Rendiconti del Seminario Matematico della Università di Padova, Tome 122 (2009) , p. 39-54
Zbl pre05663005 | MR 2582829
URL stable : http://www.numdam.org/item?id=RSMUP_2009__122__39_0

Bibliographie

[1] B. Amini - A. Amini - A. Facchini, Equivalence of diagonal matrices over local rings, J. Algebra, 320 (2008), pp. 1288-1310. MR 2427644 | Zbl 1158.16011

[2] F. W. Anderson - K. R. Fuller, Rings and Categories of Modules, Second edition, GTM 13 (Springer-Verlag, New York, 1992). MR 1245487 | Zbl 0765.16001

[3] N. V. Dung - A. Facchini, Weak Krull-Schmidt for infinite direct sums of uniserial modules, J. Algebra, 193 (1997), pp. 102-121. MR 1456570 | Zbl 0885.16008

[4] A. Facchini, Krull-Schmidt fails for serial modules, Trans. Amer. Math. Soc., 348 (1996), pp. 4561-4575. MR 1376546 | Zbl 0868.16003

[5] A. Facchini, Module Theory. Endomorphism rings and direct sum decompositions in some classes of modules, Progress in Math., 167 (Birkhäuser Verlag, Basel, 1998). MR 1634015 | Zbl 0930.16001

[6] A. Facchini - P. Prïíhoda, Monogeny dimension relative to a fixed uniform module, J. Pure Appl. Algebra, 212, no. 9 (2008), pp. 2092-2104. MR 2422193 | Zbl 1159.16003

[7] A. Facchini - P. Prïíhoda, Representations of the category of serial modules of finite Goldie dimension, in ``Models, Modules, and Abelian Groups'', R. Göbel and B. Goldsmith Eds., de Gruyter (Berlin-New York, 2008), pp. 463-486. MR 2513260 | Zbl pre05657729

[8] P. Prïíhoda, Weak Krull-Schmidt theorem and direct sum decompositions of serial modules of finite Goldie dimension,J.Algebra281,no.1(2004),pp.332-341. Zbl 1088.16008

[9] P. Prïíhoda, A version of the weak Krull-Schmidt theorem for infinite direct sums of uniserial modules, Comm. Algebra, 34, no. 4 (2006), pp. 1479-1487. MR 2224888 | Zbl 1098.16004

[10] G. Puninski, Some model theory over an exceptional uniserial ring and decompositions of serial modules, J. London Math. Soc., 64, no. 2 (2001), pp. 311-326. MR 1853453 | Zbl 1048.16003

[11] G. Puninski, Some model theory over a nearly simple uniserial domain and decompositions of serial modules, J. Pure Appl. Algebra, 163, no. 3 (2001), pp. 319-337. MR 1852123 | Zbl 1025.16005

[12] R. B. Warfield, JR., Purity and algebraic compactness for modules, Pacific J. Math., 28 (1969), pp. 699-719. MR 242885 | Zbl 0172.04801