PORTUGALIAEMATHEMATICA
Vol. 61, No. 2, pp. 193-205 (2004)
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PORTUGALIAE MATHEMATICA Vol. 61, No. 2, pp. 193-205 (2004) |
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From a single chain to a large family of submodulesLaszlo Fuchs and Sang Bum LeeDepartment of Mathematics, Tulane University,New Orleans, Louisiana 70118 -- USA E-mail: fuchs@tulane.edu Department of Mathematical Education, Sangmyung University, Seoul 110-743 -- KOREA E-mail: sblee@sangmyung.ac.kr Abstract: By making use of an ingenious idea of Paul Hill [8], we prove a general lemma showing how to obtain from a continuous well-ordered ascending chain of submodules of certain types a large collection of submodules of the same type. Several applications are exhibited. Keywords: continuous chains; $H(\k)$-family of submodules; $\k$-coherent; $RD$-submodule; pure submodule. Classification (MSC2000): 13C99, 20K99.; 20K20. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2004 Sociedade Portuguesa de Matemática
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