Michael Tsingelis

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In this paper we extend some results concerning ideals of left regular and intra-regular ordered semigroups to fuzzy ordered semigroups. A theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed. Some results on ordered groupoids-semigroups have been already given by the same authors. The aim of writing this paper is to show the(More)
It is shown that an ordered semigroup is right and left simple if and only if it does not contain proper bi-ideals. An example showing that an ordered semigroup without proper bi-ideals need not be an ordered group is constructed. Bibliography: 7 titles. The theory of semigroups based on ideals is extended to the theory of poe-semigroups based on ideal(More)
A non-empty subset I of a groupoid S is a prime (resp. semiprime) ideal of S if and only if the fuzzy ideal fI is prime (resp. semiprime). Fuzzy semigroups have been introduced by Kuroki 1, 2] as a generalization of classical semigroups, using the concept of fuzzy set introduced by Zadeh in 4]. In this short note we c haracterize the prime and semiprime(More)
Chain conditions, finiteness conditions, growth conditions, and other forms of finiteness, Noetherian rings and Artinian rings have been systematically studied for commutative rings and algebras since 1959. In pursuit of the deeper results of ideal theory in ordered groupoids (semigroups), it is necessary to study special classes of ordered groupoids(More)
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