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Radical of filters in BL‐algebras |
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| Authors: | Somayeh Motamed Lida Torkzadeh Arsham Borumand Saeid Neda Mohtashamnia |
| Institution: | 1. Department of Mathematics, Science and Research Branch, Isalamic Azad university, Kerman, Iran;2. Department of Mathematics, Isalamic Azad university, Kerman Branch, Kerman, Iran;3. Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran |
| Abstract: | 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 |
| Keywords: | BL‐algebra MV‐algebra (fantastic (positive) implicative maximal normal prime semi maximal) filter radical of a filter semi simple BL‐algebra MSC (2010) 03B47 03G25 06D99 |