Stabilizers of BE-algebras

Chapter

Abstract

A stabilizer is a part of an algebra acting on a set. Specifically, let X be any algebra operating on a set X and let A be a subset of X. The stabilizer of A, sometimes denoted St(A), is the set of elements a of A for which \(a(S)\subseteq S\). The strict stabilizer is the set of \(a\in A\) for which \(a(A) = A\). In the other words, the stabilizer of A is the transporter of A to itself. The concept of stabilizers is introduced in Hilbert algebras by I. Chajda and R. Hala\(\check{s}\) (Mult. Valued Logic 8:139–148, 2002), [37]. In this paper, the authors studied the properties of stabilizers and relative stabilizers of a given subset of a Hilbert algebra . They proved that every stabilizer of a deductive system C of \(\mathcal {H}\) is also a deductive system which is a pseudo-complement of C in the lattice of all deductive systems of \(\mathcal {H}\). In (Borumand et al., in Sci. Bull. Ser. A 74(2):65–74, 2012), [15], A. Borumand Saeid and N. Mohtashamnia constructed quotient of residuated lattices via stabilizer and studied its properties. L. Torkzadeh (Math Sci 3(2):111–132, 2009), [232] introduced dual right and dual left stabilizers in bounded BCK-algebras and investigated the relationship between of them.

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© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsMVGR College of EngineeringVizianagaramIndia

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