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On a substitution property of modules. (English) Zbl 0225.16013


MSC:

16D80 Other classes of modules and ideals in associative algebras
16D70 Structure and classification for modules, bimodules and ideals (except as in 16Gxx), direct sum decomposition and cancellation in associative algebras)
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References:

[1] Cohn, P. M.: The complement of a finitely generated direct summand of an abelian group. Proc. Amer. Math. Soc.7, 520-521 (1956). · Zbl 0070.25701 · doi:10.1090/S0002-9939-1956-0078370-X
[2] Crawley, P.: The cancellation of torsion abelian groups in direct sums. J. Algebra2, 432-442 (1965). · Zbl 0135.06004 · doi:10.1016/0021-8693(65)90004-9
[3] Fuchs, L., andF. Loonstra: On the cancellation of modules in direct sums over Dedekind domains. Indagationes Math.33, 163-169 (1971). · Zbl 0215.36802 · doi:10.1016/S1385-7258(71)80022-7
[4] Swan, R. G.: AlgebraicK-theory. Lecture Notes in Mathematics, Nr. 76. Berlin-Heidelberg-New York: Springer. 1968. · Zbl 0193.34601
[5] Walker, E. A.: Cancellation in direct sums of groups. Proc. Amer. Math. Soc.7, 898-902 (1956). · Zbl 0071.25203 · doi:10.1090/S0002-9939-1956-0081440-3
[6] Warfield, R. B. Jr.: A Krull-Schmidt theorem for infinite sums of modules. Proc. Amer. Math. Soc.22, 460-465 (1969). · Zbl 0176.31401 · doi:10.1090/S0002-9939-1969-0242886-2
[7] Warfield, R. B. Jr.: Exchange rings and decompositions of modules (to appear). · Zbl 0228.16012
[8] Wu, L. E. T., andJ. P. Jans: On quasi-projectives. Illinois J. Math.11, 439-448 (1967). · Zbl 0153.06301
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