Weak Krull-Schmidt for Infinite Direct Sums of Cyclically Presented Modules over Local Rings

Afshin Amini; Babak Amini; Alberto Facchini

Rendiconti del Seminario Matematico della Università di Padova (2009)

  • Volume: 122, page 39-54
  • ISSN: 0041-8994

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Amini, Afshin, Amini, Babak, and Facchini, Alberto. "Weak Krull-Schmidt for Infinite Direct Sums of Cyclically Presented Modules over Local Rings." Rendiconti del Seminario Matematico della Università di Padova 122 (2009): 39-54. <http://eudml.org/doc/108775>.

@article{Amini2009,
author = {Amini, Afshin, Amini, Babak, Facchini, Alberto},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {direct sums of cyclically presented modules over local rings; Krull-Schmidt theorem; direct sums of modules; epigeny classes; direct summands},
language = {eng},
pages = {39-54},
publisher = {Seminario Matematico of the University of Padua},
title = {Weak Krull-Schmidt for Infinite Direct Sums of Cyclically Presented Modules over Local Rings},
url = {http://eudml.org/doc/108775},
volume = {122},
year = {2009},
}

TY - JOUR
AU - Amini, Afshin
AU - Amini, Babak
AU - Facchini, Alberto
TI - Weak Krull-Schmidt for Infinite Direct Sums of Cyclically Presented Modules over Local Rings
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2009
PB - Seminario Matematico of the University of Padua
VL - 122
SP - 39
EP - 54
LA - eng
KW - direct sums of cyclically presented modules over local rings; Krull-Schmidt theorem; direct sums of modules; epigeny classes; direct summands
UR - http://eudml.org/doc/108775
ER -

References

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  1. [1] B. AMINI - A. AMINI - A. FACCHINI, Equivalence of diagonal matrices over local rings, J. Algebra, 320 (2008), pp. 1288-1310. Zbl1158.16011MR2427644
  2. [2] F. W. ANDERSON - K. R. FULLER, Rings and Categories of Modules, Second edition, GTM 13 (Springer-Verlag, New York, 1992). Zbl0765.16001MR1245487
  3. [3] N. V. DUNG - A. FACCHINI, Weak Krull-Schmidt for infinite direct sums of uniserial modules, J. Algebra, 193 (1997), pp. 102-121. Zbl0885.16008MR1456570
  4. [4] A. FACCHINI, Krull-Schmidt fails for serial modules, Trans. Amer. Math. Soc., 348 (1996), pp. 4561-4575. Zbl0868.16003MR1376546
  5. [5] A. FACCHINI, Module Theory. Endomorphism rings and direct sum decompositions in some classes of modules, Progress in Math., 167 (Birkhäuser Verlag, Basel, 1998). Zbl0930.16001MR1634015
  6. [6] A. FACCHINI - P. PRÏÍHODA, Monogeny dimension relative to a fixed uniform module, J. Pure Appl. Algebra, 212, no. 9 (2008), pp. 2092-2104. Zbl1159.16003MR2422193
  7. [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. Zbl1221.16009MR2513260
  8. [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. Zbl1088.16008
  9. [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. Zbl1098.16004MR2224888
  10. [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. Zbl1048.16003MR1853453
  11. [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. Zbl1025.16005MR1852123
  12. [12] R. B. WARFIELD, JR., Purity and algebraic compactness for modules, Pacific J. Math., 28 (1969), pp. 699-719. Zbl0172.04801MR242885

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