Some new filters and their properties on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mstyle mathvariant="normal"><mml:mi>BL</mml:mi></mml:mstyle></mml:math>-algebras

In this paper we introduce the notion of a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mstyle mathvariant="normal"><mml:mi>DC</mml:mi></mml:mstyle></mml:math>-prime filter in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mstyle mathvariant="normal"><mml:mi>BL</mml:mi></mml:mstyle></mml:math>-algebras and obtain some theorems in order to determine the relationships between this notion and some types of filters in a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mstyle mathvariant="normal"><mml:mi>BL</mml:mi></mml:mstyle></mml:math>-algebra. By some examples, we show that each of these concepts is different from the other. Also, using the notion of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mstyle mathvariant="normal"><mml:mi>DC</mml:mi></mml:mstyle></mml:math>-prime filters, a new class of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mstyle mathvariant="normal"><mml:mi>BL</mml:mi></mml:mstyle></mml:math>-algebras are defined and studied.