Soft Computing

, Volume 21, Issue 3, pp 687–698 | Cite as

A new class of BL-algebras

Foundations
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Abstract

In this paper, we introduce the notion of right stabilizers in BL-algebras and define a class of BL-algebras, called RS-BL-algebra. Then we investigate the relationships between the right and left stabilizers in BL-algebras. After that we define the concept of semi RS-BL-algebras and we prove that semisimple BL-algebras and semi RS-BL-algebras are RS-BL-algebra. Moreover, every finite RS-BL-algebra is a semi RS-BL-algebra. Finally, we introduce the concept of a semi-stabilizer and a stabilizer filter in a BL-algebra and we state and prove some theorems which determine the relationships between this notion and the other types of filters of a BL-algebra.

Keywords

RS-BL-algebra Semi RS-BL-algebra Right (left) stabilizer Semi stabilizer filter, Stabilizer filter  

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsBandar Abbas BranchBandar AbbasIran
  2. 2.Department of MathematicsKerman Branch, Islamic Azad UniversityKermanIran

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