A study of stabilizers in triangle algebras

ABsTRAcpaper,In. the notions of stabilizer of a subset and the stabilizer of a subset with respect mother one in triangle algebras and study them in details. It is shown that the stabilizer of a subset and stabilizer of an interval valued residuated lattice filter (IVRL-filter) with respect to another INTRL-filter are [IVRL-filters. We state and proti some theorems which determine some properties of this stabilizers in triangle algebras. Also, we prove that in linearly ordered triangle algebras, stabilizer of a set is an IVRL-extended prime filter. Finally, we consider the influence of stabilizers on product and quotient triangle algebras. (C) 2018 Mathematical Institute Slovak Academy of Sciences