Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 61, No. 2, pp. 193-205 (2004)

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From a single chain to a large family of submodules

Laszlo Fuchs and Sang Bum Lee

Department 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.

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Electronic version published on: 7 Mar 2008.

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