Publications de l'Institut Mathématique, Nouvelle Série Vol. 81(95), pp. 95–102 (2007) 

ON REGULAR ANTICONGRUENCE IN ANTIORDERED SEMIGROUPSDaniel Abraham RomanoPrirodnomatematicki fakultet, 78000 Banja Luka, Srpska, Bosnia and HerzegovinaAbstract: For an anticongruence $q$ we say that it is regular anticongruence on semigroup $(S,=,\neq,\cdot,\alpha)$ ordered under antiorder $\alpha$ if there exists an antiorder $\theta$ on $S/q$ such that the natural epimorphism is a reverse isotone homomorphism of semigroups. Anticongruence $q$ is regular if there exists a quasiantiorder $\sigma$ on $S$ under $\alpha$ such that $q=\sigma\cup\sigma^{1}$. Besides, for regular anticongruence $q$ on $S$, a construction of the maximal quasiantiorder relation under $\alpha$ with respect to $q$ is shown. Keywords: Constructive mathematics, semigroup with apartness, antiordered semigroup, anticongruence, regular anticongruence, quasiantiorder Classification (MSC2000): 03F65; 06F05, 20M10 Full text of the article: (for faster download, first choose a mirror)
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