A study of stabilizers in triangle algebras

Year, pages: 2018, 41 - 52

In this paper, we introduce the notions of stabilizer of a subset and the stabilizer of a subset with respect to another 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 IVRL-filter are IVRL-filters. We state and prove 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.

Zahiri, S., Saeid, A., Eslami, E. 2018. A study of stabilizers in triangle algebras. In Mathematica Slovaca, vol. 68, no.1, pp. 41-52. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0078

Zahiri, S., Saeid, A., Eslami, E. (2018). A study of stabilizers in triangle algebras. Mathematica Slovaca, 68(1), 41-52. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0078