• 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.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.1-10
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• 2004

We here consider necessary and sufficient conditions for a completely right injective semigroup S whose lattice Ｌ(S) of right congruences on S is semiatomic. These are preceded by a number of results on the characterization of a semigroup S in which every automaton over S is injective(called a completely right injective semigroup).