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A new class of BL-algebras

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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.

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Acknowledgments

The authors would like to express their thanks to the referees for their comments and suggestions which improved the paper. This paper obtain from research project of first author that has been financially supported by the office of vice chancellor for research of Islamic Azad University, Bandar Abbas Branch.

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Authors and Affiliations

  1. Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran

    Somayeh Motamed

  2. Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran

    Lida Torkzadeh

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  1. Somayeh Motamed
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  2. Lida Torkzadeh
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Correspondence to Somayeh Motamed.

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The authors declare that there are no conflict of interest.

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Communicated by A. Di Nola.

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Motamed, S., Torkzadeh, L. A new class of BL-algebras. Soft Comput 21, 687–698 (2017). https://doi.org/10.1007/s00500-016-2043-z

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