Abstract:In this paper, we study the ordered regular equivalence relations on ordered semihypergroups in detail. To begin with, we introduce the concept of weak pseudoorders on an ordered semihypergroup, and investigate several related properties. In particular, we construct an ordered regular equivalence relation on an ordered semihypergroup by a weak pseudoorder. As an application of the above result, we completely solve the open problem on ordered semihypergroups introduced in [B. Davvaz, P. Corsini and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseuoorders, European J. Combinatorics 44 (2015), 208-217]. Furthermore, we establish the relationships between ordered regular equivalence relations and weak pseudoorders on an ordered semihypergroup, and give some homomorphism theorems of ordered semihypergroups, which are generalizations of similar results in ordered semigroups.
Abstract:In this paper, we introduce GP-po-flatness property of S -posets over a pomonoid S , which lies strictly between principal weak po-flatness and po-torsion freeness. Furthermore, we investigate the homological classification problems of pomonoids by using this new property. Finally, we consider direct products of GP-po-flat S-posets. As an application, characterizations of pomonoids over which direct products of nonempty families of principally weakly po-flat S-posets are principally weakly po-flat are obtained, and some results of Khosravi, R. in a certain extent are generalized.
Abstract. Let P ϕ (n,b,λ ) denote the class of normalized univalent functions f (z) = z + a 2 z 2 + ..., which are defined in the unit disk Δ and satisfying 1, where ϕ(z) is the function with positive real part, D n f denotes the sȃlȃgean operator, n 0 , 0 λ 1 , b ∈ C . In this paper, for the class P ϕ (n,b,λ ) , the Fekete-Szegö inequalities are completely solved. A more general class K (β ,n,λ ,g(z)) related P ϕ (n,b,λ ) is also considered with same subject, which extends the earlier corresponding results for the class of strongly close-to-convex functions of order β .Mathematics subject classification (2010): 30C45, 30C50.
In this paper, we give some characterizations of 𝓠-regular semigroups and show that the class of 𝓠-regular semigroups is closed under the direct product and homomorphic images. Furthermore, we characterize the 𝓠-subdirect products of this class of semigroups and study the E-unitary 𝓠-regular covers for 𝓠-regular semigroups, in particular for those whose maximum group homomorphic image is a given group. As an application of these results, we claim that the similar results on V-regular semigroups also hold.
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