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Radical of filters in BL ‐algebras
Author(s) -
Motamed Somayeh,
Torkzadeh Lida,
Saeid Arsham Borumand,
Mohtashamnia Neda
Publication year - 2011
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201010003
Subject(s) - mathematics , filter (signal processing) , simple (philosophy) , algebra over a field , pure mathematics , state (computer science) , discrete mathematics , algorithm , computer science , epistemology , philosophy , computer vision
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 D s ( 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