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An investigation on Boolean prime filters in BL-algebras

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Abstract

In this paper, by considering the notion of basic logic (BL)-algebras, we study some properties of Boolean prime filters. In fact, we concern a relationship between the important theorems in commutative algebra and BL-algebra theory. We prove the BL-version of the going up and lying over theorems in BL-algebras theory with respect to Boolean prime filters. Also, we study the notion of localization in BL-algebras theory.

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Acknowledgments

The authors are highly grateful to referees for their valuable comments and suggestions for improving the paper.

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Authors and Affiliations

  1. Department of Mathematics, Persian Gulf University, 75169, Bushehr, Iran

    Saeed Rasouli

  2. Department of Mathematics, Yazd University, Yazd, Iran

    Bijan Davvaz

Authors
  1. Saeed Rasouli
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  2. Bijan Davvaz
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Correspondence to Bijan Davvaz.

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Communicated by B. Gerla.

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Rasouli, S., Davvaz, B. An investigation on Boolean prime filters in BL-algebras. Soft Comput 19, 2743–2750 (2015). https://doi.org/10.1007/s00500-015-1711-8

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  • DOI: https://doi.org/10.1007/s00500-015-1711-8

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