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- W2073687777 abstract "Abstract Let Sing n be the semigroup of all singular full transformations on the set X n = {1, 2,…, n} under the composition of functions. Let E(J n − 1) be the set of all idempotents of the top 𝒥-class J n − 1 = {α ∈ Sing n :|im α| = n-1}. For any nonempty subset I of E(J n − 1), the aim of this paper is to find a constructive necessary and sufficient condition for the semiband S(I) = ⟨I⟩ to be ℋ-trivial. Further, the semiband S(I) is locally maximal ℋ-trivial if S(I) is ℋ-trivial and S(I ∪ {e}) is not ℋ-trivial for any e ∈ E(J n − 1 )I. As applications, we classify locally maximal ℋ-trivial subsemibands and locally maximal regular ℋ-trivial subsemibands of Sing n , respectively. Moreover, the characterization of which S(I) is a band is obtained. #Communication by P. Higgins" @default.
- W2073687777 created "2016-06-24" @default.
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- W2073687777 date "2005-04-01" @default.
- W2073687777 modified "2023-10-18" @default.
- W2073687777 title "ℋ-Trivial Transformation Semibands and Digraphs" @default.
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- W2073687777 doi "https://doi.org/10.1081/agb-200060529" @default.
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