Primary Filters in BL-algebras
Somayeh Motamed, Javad Moghaderi · New Mathematics and Natural Computation · 2019
In this paper, we defined the prime-like filters of [Formula: see text]-algebras, and proved some relations between this filter and other types of filters in [Formula: see text]-algebras. Also, we found the relation between prime-like filters and constructed the quotient [Formula: see text]-algebras via this filter. We proved some results that have proven for prime filters of [Formula: see text]-algebras, to the case of prime-like filters of [Formula: see text]-algebras. In this way, we found new properties for the primary filters of [Formula: see text]-algebras. Also, we introduced the notions of prime-like [Formula: see text]-algebras ([Formula: see text]-algebras), and Top-like [Formula: see text]-algebras. And we applied the notion of prime-like filters to define and study a new topology on [Formula: see text]-algebras.