Radical of filters in BL -algebras
Somayeh Motamed, Lida Torkzadeh, Arsham Borumand Saeid, Neda Mohtashamnia · Mathematical logic quarterly · 2011
In this paper, the notion of the radical of a filter in BL-algebras is defined and several characterizations of the radical of a filter are given. Also we prove that A/F is an MV-algebra if and only if Ds(A) ⊆ F. After that we define the notion of semi maximal filter in BL-algebras and we state and prove some theorems which determine the relationship between this notion and the other types of filters of a BL-algebra. Moreover, we prove that A/F is a semi simple BL-algebra if and only if F is a semi maximal filter of A. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim