• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.563-571
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• 1997

In this paper we define CR(completely reachable), MICR(minimal cyclic refinement)and MACR(maximal cyclic 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.

• 대한수학회지
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• 제35권1호
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• pp.1-9
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• 1998

In this paper we define CR(completely reachable), MICR(minimal cyclic refinement) and MACR(maximal cyclic 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.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.663-670
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• 2005

In this paper we shall give some decompositions derived from cyclic subautomata or neighborhoods of the automaton. Also we shall discuss some characterizations of cyclic automata when an automaton is maximal cyclic refinement. If m $\in$ M is totally reachable state, we shall see that {$mX^{\ast}$} is minimal.