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Filters by BL-homomorphisms

  • Fatemeh Najmi Dolat Abadi
  • Javad MoghaderiEmail author
Foundations
  • 5 Downloads

Abstract

In this paper, the notions of \(\sigma \)-filters, \(\sigma \)-invariant filters, \(\sigma \)-primary filters and \(\sigma \)-rigid BL-algebras are introduced. Some basic properties and results are given with respect to these notions. The properties of the space of all prime \(\sigma \)-invariant filters of a BL-algebra \((\hbox {Spec}^{\sigma }(L))\) are observed. Moreover, it is shown that under some conditions, \(\hbox {Spec}^{\sigma }(L)\) is Hausdorff if and only if it is a \(T_{1}\)-space.

Keywords

(Integral, \(\sigma \)-rigid) BL-algebra Godel algebra MV-algebra (obstinate, implicative, prime, \(\sigma \)-invariant and maximal) filter \(\sigma \)-Filter 

Notes

Acknowledgements

The authors would like to express their thanks to the referees for their comments and suggestions which improved the paper.

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HormozganBandar AbbasIran

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