Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
almost-flat module; self-small module; endomorphism ring
almost-flat module; self-small module; endomorphism ring
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.
References:
[1] U. Albrecht: Endomorphism rings of faithfully flat abelian groups. Res. Math. 17 (1990), 179–201. DOI 10.1007/BF03322457 | MR 1052585 | Zbl 0709.20031
[2] U. Albrecht: Endomophism rings, tensor product and Fuchs problem 47. Contemp. Math. 130 (1992), 17–31. DOI 10.1090/conm/130/1176107 | MR 1176107
[3] U. Albrecht and P. Goeters: Almost flat abelian groups. Rocky Mountain J. Math. 25 (1993), 827–842. MR 1357094
[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
[5] H. Cartan and S. Eilenberg: Homological Algebra. Oxford University Press, Oxford, 1956. MR 0077480
[6] F. Richman and E. A. Walker: Cyclic Ext. Rocky Mountain J. Math. 11 (1981), 611–615. DOI 10.1216/RMJ-1981-11-4-611 | MR 0639446
[7] B. Stenstrom: Ring of Quotients. An Introduction to Methods of Ring Theory. Springer-Verlag, Berlin-Heidelberg-New York, 1975. MR 0389953
[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
[9] R. Wisbauer: Foundations of Module and Ring Theory. Gordon and Breach, Philadelphia, 1986. MR 1144522
[10] R. Wisbauer: Static modules and equivalences. (1998), Preprint. MR 1761573
Search
Partner of
