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On Generalized Annihilators in BL-Algebras

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Quantitative Logic and Soft Computing 2016

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 510))

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Abstract

The theory of generalized annihilators on BL-algebras are developed in this paper. Firstly, some properties of generalized annihilators on BL-algebras are supplemented. Secondly, we introduce the notion of involutory ideals relative to an ideal I and denote the set of all of them by \(S_{I}(L)\). Then \(S_{I}(L)\) can be made into a complete Boolean lattice and a BL-algebra with respect to the suit operations, respectively. Finally, the prime ideals can be characterized by the generalized annihilators, and the generalized annihilators of the quotient algebra induced by an ideal I in a BL-algebra L are studied.

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Acknowledgments

This research is supported by a grant of National Natural Science Foundation of China (11571281).

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710127, People’s Republic of China

    Yu-Xi Zou & Xiao-Long Xin

  2. Department of Mathematics Education, Gyeongsang National University, Chinju, 660-701, Korea

    Young-Bae Jun

Authors
  1. Yu-Xi Zou
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  2. Xiao-Long Xin
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  3. Young-Bae Jun
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Corresponding author

Correspondence to Xiao-Long Xin .

Editor information

Editors and Affiliations

  1. Zhejiang, Zhejiang Sci-Tech University Zhejiang, Hangzhou, China

    Tai-He Fan

  2. Fujian, Jimei University Fujian, Xiamen, China

    Shui-Li Chen

  3. Zhejiang, Zhejiang Sci-Tech University Zhejiang, Hangzhou, China

    San-Min Wang

  4. Yanta, Shaanxi Normal University Yanta, Xi’an, China

    Yong-Ming Li

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Zou, YX., Xin, XL., Jun, YB. (2017). On Generalized Annihilators in BL-Algebras. In: Fan, TH., Chen, SL., Wang, SM., Li, YM. (eds) Quantitative Logic and Soft Computing 2016. Advances in Intelligent Systems and Computing, vol 510. Springer, Cham. https://doi.org/10.1007/978-3-319-46206-6_43

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  • DOI: https://doi.org/10.1007/978-3-319-46206-6_43

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46205-9

  • Online ISBN: 978-3-319-46206-6

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