Semigroups of Transformations Preserving an Equivalence Relation and a Cross-Section

نویسندگان

  • João Araújo
  • Janusz Konieczny
چکیده

For a set X , an equivalence relation ρ on X , and a cross-section R of the partition X/ρ induced by ρ, consider the semigroup T (X, ρ, R) consisting of all mappings a from X to X such that a preserves both ρ (if (x, y) ∈ ρ then (xa, ya) ∈ ρ) and R (if r ∈ R then ra ∈ R). The semigroup T (X, ρ, R) is the centralizer of the idempotent transformation with kernel ρ and imageR. We determine the structure of T (X, ρ, R) in terms of Green’s relations, describe the regular elements of T (X, ρ, R), and determine the following classes of the semigroups T (X, ρ, R): regular, abundant, inverse, and completely regular. 2000 Mathematics Subject Classification: 20M20.

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تاریخ انتشار 2015