• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.671-678
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• 2005

In this paper we shall give some characterizations of strongly cyclic and totally reachable (TR) automata when A = (M, X, $\delta$) is MinCR-automaton. Also we shall see that if an automaton A is strongly cyclic, then A is cyclic and a TR-automaton. When A is MinmaxCR-automaton, we shall give another characterizations for a strongly cyclic and cyclic TR-automaton.

• The Pure and Applied Mathematics
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• v.9 no.2
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• pp.119-128
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• 2002

We here characterize semigroups (which are called completely right projective semigroups) for which every S-automaton is projective, and then examine some of the relationships with the semigroups (which are called completely right injective semigroups) in which every S-automaton is injective.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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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.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.595-604
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• 2004

In this paper We shall give some characterizations for mX＊ derived from the relationships between S(m) and C(m). Also we shall discuss the minimal, maximal, strongly cyclic and minmaxCR-automata. There is an interesting part for the relationship between mX＊ and S(m). That is to say, that mX＊ is minimal has the same meaning as S(m) is strongly cyclic. We shall note that the minimality implies ‘ strongly cyclic’ and ‘strongly cyclic’ implies ‘cyclic’ and ‘cyclic’ implies ‘a MaxCR-automaton’.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.747-756
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• 1999

In ring theory it is well-known that a ring R is (von Neumann) regular if and only if all right R-modules are flat. But the analogous statement for this result does not hold for a monoid S. Hence, in sense of S-acts, Liu (]10]) showed that, as a weak analogue of this result, a monoid S is regular if and only if all left S-acts satisfying condition (E) ([6]) are flat. Moreover, Bulmann-Fleming ([6]) showed that x is a regular element of a monoid S iff the cyclic right S-act S/p(x, x2) is flat. In this paper, we show that the analogue of this result can be held for automata and them characterize regular semigroups by flat automata.