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

• Articles • Previous Articles     Next Articles

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

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
[1] . The number of homomorphisms from metacyclic groups to metacyclic groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 17-22.
[2] LIU Chun-hui. Lattice of(,∨(-overq))-fuzzy filters in a BL-algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 104-110.
[3] PENG Jia-yin. Disturbing fuzzy ideals of BL-algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 78-94.
[4] BO Chun-xin, YAO Bing-xue. (λ, μ)-anti-fuzzy rough subgroup [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 23-27.
[5] YANG Yong-wei, HE Peng-fei, LI Yi-jun. Falling fuzzy ideals of BL-algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 83-89.
[6] LIU Chun-hui. Theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 83-89.
[7] YANG Yong-wei1, 2, HE Peng-fei2, LI Yi-jun2,3. On strict filters of BL-algebras#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 63-67.
[8] ZHAO Zhi-qin. FS-basis under one-sided monomial orderings [J]. J4, 2013, 48(2): 36-41.
[9] ZHOU Jian-ren, WU Hong-bo*. The regularness of WBR0-algebras and relationship with other logic algebras [J]. J4, 2012, 47(2): 86-92.
[10] LIU Lu-lu1, FU Wen-qing2, LI Sheng-gang1*. Characterizations of fuzzy subinclines, fuzzy ideals, fuzzy filters and fuzzy congruence relations [J]. J4, 2011, 46(11): 48-52.
[11] LIU Chun-hui1, XU Luo-shan2. On ideals of residuated lattices [J]. J4, 2010, 45(4): 66-71.
[12] QIN Xue-cheng, LIU Chun-hui*. Fuzzy ⊙-ideals in regular residuated lattices [J]. J4, 2010, 45(10): 66-70.
[13] LIU Hong-ping,MENG Guang-wu . The *-coparacompactness in L-bitopological spaces [J]. J4, 2008, 43(4): 42-46 .
[14] LIU Hong-ping,MENG Guang-wu . F*-Paracompactness in L-topological spaces [J]. J4, 2008, 43(3): 75-79 .
[15] CHEN Bin . The expandability of WNspace [J]. J4, 2006, 41(5): 48-50 .
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!