Journal
MATHEMATICAL LOGIC QUARTERLY
Volume 57, Issue 2, Pages 166-179Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/malq.201010003
Keywords
BL-algebra; MV-algebra; (fantastic, (positive) implicative, maximal, normal, prime, semi; maximal) filter; radical of a filter; semi simple BL-algebra
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Funding
- Shahid Bahonar University of Kerman, Iran
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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) subset of 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. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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