# CHARACTERIZATION OF SEMIGROUPS BY FLAT AUTOMATA

• Lee, O. (Department of Mathematics Ewha Womans University) ;
• Shin, D.W. (Department of Mathematics Ewha Womans University)
• Published : 1999.07.01
• 52 10

#### Abstract

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.

#### Keywords

flat automaton;cyclic automaton;principal right congruence;regular semigroup

#### References

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