JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (2): 36-41.doi: 10.6040/j.issn.1671-9352.0.2013.294

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The prime reverse deductive system of locally finite #br# BL-algebras with properties

WEN Xian-hong, WU Hong-bo*   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, Shaanxi, China
  • Received:2013-06-18 Online:2014-02-20 Published:2014-06-04

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Abstract:

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.

Key words: reverse deductive system, congruence relation, BL-algebra, quotient algebra, locally finite, prime reverse deductive system

CLC Number: 

  • O141.1
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