• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.1-14
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• 2005

The aim of this paper is to study order-congruences on a S-poset A and to characterize the order-congruences by the concepts of pseudooreders on A and quasi-chains module a congruence p. Some homomorphism theorems of S-posets are given which is similar to the one of ordered semigroups. Finally, It is shown that there exists the non-trivial order-congruence on a S-poset by an example.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.217-226
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• 1999

In this paper we define automata-linearly independence. An automaton M has a basis B iff M is free provided that we assume that the action of S on X $\times$ S is (x,sa) for all a, s $\in$ S and x $\in$ X. if a semigroup S is PRID every subautomaton of a free S-automaton is free.

• Journal of applied mathematics & informatics
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• v.9 no.2
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• pp.705-716
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• 2002

In this paper we shall introduce the algebraic structure of a tensor product for arbitrarily given automata, giving a defintion of the tensor product for automata. We introduce and study that for any set X there always exists a free automaton on X. The existence of a tensor product for automata will be investigated in the same way like modules do.