Title:
|
Almost-flat modules (English) |
Author:
|
Breaz, Simion |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
53 |
Issue:
|
2 |
Year:
|
2003 |
Pages:
|
479-489 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
We present general properties for almost-flat modules and we prove that a self-small right module is almost flat as a left module over its endomorphism ring if and only if the class of $g$-static modules is closed under the kernels. (English) |
Keyword:
|
almost-flat module |
Keyword:
|
self-small module |
Keyword:
|
endomorphism ring |
MSC:
|
16D40 |
MSC:
|
16E30 |
MSC:
|
20K40 |
idZBL:
|
Zbl 1027.16001 |
idMR:
|
MR1983467 |
. |
Date available:
|
2009-09-24T11:03:32Z |
Last updated:
|
2020-07-03 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127815 |
. |
Reference:
|
[1] U. Albrecht: Endomorphism rings of faithfully flat abelian groups.Res. Math. 17 (1990), 179–201. Zbl 0709.20031, MR 1052585, 10.1007/BF03322457 |
Reference:
|
[2] U. Albrecht: Endomophism rings, tensor product and Fuchs problem 47.Contemp. Math. 130 (1992), 17–31. MR 1176107, 10.1090/conm/130/1176107 |
Reference:
|
[3] U. Albrecht and P. Goeters: Almost flat abelian groups.Rocky Mountain J. Math. 25 (1993), 827–842. MR 1357094 |
Reference:
|
[4] D. M. Arnold and C. E. Murley: Abelian groups $A$, such that $\mathop {\mathrm Hom}(A,-)$ preserves direct sums of copies of $A$.Pacific J. Math. 56 (1975), 7–20. MR 0376901 |
Reference:
|
[5] H. Cartan and S. Eilenberg: Homological Algebra.Oxford University Press, Oxford, 1956. MR 0077480 |
Reference:
|
[6] F. Richman and E. A. Walker: Cyclic Ext.Rocky Mountain J. Math. 11 (1981), 611–615. MR 0639446, 10.1216/RMJ-1981-11-4-611 |
Reference:
|
[7] B. Stenstrom: Ring of Quotients. An Introduction to Methods of Ring Theory.Springer-Verlag, Berlin-Heidelberg-New York, 1975. MR 0389953 |
Reference:
|
[8] C. Visonhaler and W. Wickless: Homological dimensions of completely decomposable groups.Lecture Notes in Pure and Appl. Math. 146 (1993), 247–258. MR 1217276 |
Reference:
|
[9] R. Wisbauer: Foundations of Module and Ring Theory.Gordon and Breach, Philadelphia, 1986. MR 1144522 |
Reference:
|
[10] R. Wisbauer: Static modules and equivalences.(1998), Preprint. MR 1761573 |
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