首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Strong NMV-algebras, commutative basic algebras and naBL-algebras
Authors:Xiaohong Zhang
Institution:1. Department of Mathematics College of Arts and Sciences, Shanghai Maritime University, Shanghai, 201306, P. R. China
Abstract:The aim of the paper is to investigate the relationship among NMV-algebras, commutative basic algebras and naBL-algebras (i.e., non-associative BL-algebras). First, we introduce the notion of strong NMV-algebra and prove that
  1. a strong NMV-algebra is a residuated l-groupoid (i.e., a bounded integral commutative residuated lattice-ordered groupoid)
  2. a residuated l-groupoid is commutative basic algebra if and only if it is a strong NMV-algebra.
Secondly, we introduce the notion of NMV-filter and prove that a residuated l-groupoid is a strong NMV-algebra (commutative basic algebra) if and only if its every filter is an NMV-filter. Finally, we introduce the notion of weak naBL-algebra, and show that any strong NMV-algebra (commutative basic algebra) is weak naBL-algebra and give some counterexamples.
Keywords:
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号