Strong identities and fortification in transposition hypergroups

  title={Strong identities and fortification in transposition hypergroups},
  author={James Jantosciak and Massouros Ch.G.},
Abstract An element e in a hypergroup H is a strong identity if x ∈ ex = xe ⊂ x ⋃ e. The elements of H separate into two classes, the set A = {x ∈ H | ex = xe = x ⋃ e}, including e, of attractive elements and the set C = {x ∈ H – e | ex = xe = x} of canonical elements. If H is a transposition hypergroup then A is shown to be a closed subhypergroup of essentially indistinguishable elements. The structure of H is then determined, for A can be contracted into e leaving the “resulting” C ⋃ e, which… CONTINUE READING