%A WEN Xian-hong, WU Hong-bo* %T The prime reverse deductive system of locally finite #br# BL-algebras with properties %0 Journal Article %D 2014 %J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) %R 10.6040/j.issn.1671-9352.0.2013.294 %P 36-41 %V 49 %N 2 %U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_2339.shtml} %8 2014-02-20 %X

Firstly, the concepts of reverse deductive system and prime reverse deductive system are introduced to BL-algebra. The basic properties of prime reverse deductive system and the relationship between reverse deductive and common ideal in locally finite BL-algebras are investigated. Secondly, the connection between reverse deductive system and congruence relations is discussed. At last, it is proved that the quotient algebra determined by prime reverse deductive system is linear BL-algebra, and that in a locally finite BL-algebra a reverse deductive system is prime reverse deductive system if and only if the quotient algebra determined by itself is a linear BL-algebra.