Primary Filters in BL-algebras

Somayeh Motamed and Javad Moghaderi ()
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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

New Mathematics and Natural Computation (NMNC), 2019, vol. 15, issue 03, 447-461

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.

Keywords: BL-algebras; prime-like filter; primary filter (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S179300571950025X

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