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J. Korean Math. Soc. 1998; 35(1): 1-9

Printed March 1, 1998

Copyright © The Korean Mathematical Society.

Strong-max cyclic submodules

Chin-Hong Park

Sunmoon University

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In this paper we define CR(completely reachable), \noindent MICR(minimal \ cyclic \ refinement) \ and \ MACR(maximal \ cyclic\\ \noindent refinement)-Modules. We have obtained equivalent statements for minimal cyclic submodule and maximal cyclic submodule. Also, we have obtained necessary and sufficient conditions for a module M with MICR to be cyclic or strongly cyclic.

Keywords: completely reachable, minimal cyclic refinement, maximal cyclic refinement, strongly cyclic module

MSC numbers: 16D99

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