| Title:
|
$A$-projective resolutions and an Azumaya theorem for a class of mixed abelian groups (English) |
| Author:
|
Albrecht, Ulrich |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
73-93 |
| . |
| Category:
|
math |
| . |
| MSC:
|
20K21 |
| MSC:
|
20K25 |
| MSC:
|
20K27 |
| MSC:
|
20K40 |
| idZBL:
|
Zbl 1079.20503 |
| idMR:
|
MR1814634 |
| . |
| Date available:
|
2009-09-24T10:40:03Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127628 |
| . |
| Reference:
|
[ALBR] U. Albrecht: Endomorphism rings of faithfully flat abelian groups of infinite rank.Results Math. 17 (1990), 179–201. MR 1052585, 10.1007/BF03322457 |
| Reference:
|
[ALBR3] U. Albrecht: On the construction of $A$-solvable abelian groups.Czechoslovak Math. J. 44 (1994), 413–430. MR 1288162 |
| Reference:
|
[AGW] U. Albrecht, H. P. Goeters and W. Wickless: The flat dimension of mixed abelian groups as $E$-modules.Rocky Mountain J. Math. 25 (1995), 569–590. MR 1336551, 10.1216/rmjm/1181072238 |
| Reference:
|
[AF] F. Anderson and K. Fuller: Rings and Categories of Modules.Springer Verlag, 1992. MR 1245487 |
| Reference:
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[Ar] D. Arnold: Abelian groups flat over their endomorphism ring.Preprint. |
| Reference:
|
[AHR] D. Arnold, R. Hunter and F. Richman: Global Azumaya theorems in additive categories.J. Pure Appl. Algebra 16 (1980), 232–242. MR 0558485, 10.1016/0022-4049(80)90026-2 |
| Reference:
|
[AL] D. Arnold and L. Lady: Endomorphism rings and direct sums of torsion-free abelian groups.Trans. Amer. Math. Soc. 211 (1975), 225–237. MR 0417314, 10.1090/S0002-9947-1975-0417314-1 |
| Reference:
|
[B] R. Baer: Abelian groups without elements of finite order.Duke Math. J. 3 (1937), 68–122. Zbl 0016.20303, MR 1545974, 10.1215/S0012-7094-37-00308-9 |
| Reference:
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[DG] M. Dugas and R. Goebel: Every cotorsion-free ring is an endomorphism ring.Proc. London Math. Soc. 45 (1982), 319–336. MR 0670040 |
| Reference:
|
[Fu] L. Fuchs: Infinite Abelian Groups.Academic Press, New York, London, 1970/73. MR 0255673 |
| Reference:
|
[GW] S. Glaz and W. Wickless: Regular and principal projective endomorphism rings of mixed abelian groups.(to appear). MR 1261253 |
| Reference:
|
[Gr] P. Griffith: Infinite Abelian Groups.Chicago Lectures in Mathematics, 1970. MR 0289638 |
| Reference:
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[HRW] R. Hunter, F. Richman and E. Walker: Warfield modules.LNM 616, Springer, 1977, pp. 87–139. MR 0506216 |
| Reference:
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[Ka] I. Kaplansky: Projective modules.Ann. of Math. 68 (1958), 372–377. Zbl 0083.25802, MR 0100017, 10.2307/1970252 |
| Reference:
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[Ku] L. Kulikov: On direct decompositions of groups.Ukrain. Mat. Zh. 4 (1952), 230–275, 347–372. MR 0058598 |
| Reference:
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[ST] B. Stenström: Ring of Quotients.Springer Verlag, Berlin, Heidelberg, New York, 1975. MR 0389953 |
| Reference:
|
[U] F. Ulmer: A flatness criterion in Grothendick categories.Invent. Math. 19 (1973), 331–336. MR 0335601, 10.1007/BF01425418 |
| Reference:
|
[W] W. Wickless: A functor from mixed groups to torsion-free groups.Contemp. Math. 171 (1994), 407–417. Zbl 0821.20036, MR 1293158, 10.1090/conm/171/01792 |
| . |
