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Primary Filters in BL-algebras

Author

Listed:
  • Somayeh Motamed

    (Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran)

  • Javad Moghaderi

    (Department of Mathematics, University of Hormozgan, Bandar Abbas, Iran)

Abstract

In this paper, we defined the prime-like filters of BL-algebras, and proved some relations between this filter and other types of filters in BL-algebras. Also, we found the relation between prime-like filters and constructed the quotient BL-algebras via this filter. We proved some results that have proven for prime filters of BL-algebras, to the case of prime-like filters of BL-algebras. In this way, we found new properties for the primary filters of BL-algebras. Also, we introduced the notions of prime-like BL-algebras (Pl−BL-algebras), and Top-like BL-algebras. And we applied the notion of prime-like filters to define and study a new topology on BL-algebras.

Suggested Citation

  • Somayeh Motamed & Javad Moghaderi, 2019. "Primary Filters in BL-algebras," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 447-461, November.
  • Handle: RePEc:wsi:nmncxx:v:15:y:2019:i:03:n:s179300571950025x
    DOI: 10.1142/S179300571950025X
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