International Journal of Theoretical Physics

, Volume 50, Issue 4, pp 1175–1185 | Cite as

Pseudo Weak Effect Algebras and Pseudo Weak D-posets



Pseudo weak effect algebras are base on an noncommutative, associative and cancellative partial addition, but in general not determined by it. Every pseudo BL-algebra gives rise to a pseudo weak effect algebra.

We introduce two different operations in pseudo weak effect algebras and also in the pseudo weak difference posets. We prove that the pseudo weak effect algebras and the pseudo weak difference posets are the same thing.

We give the exact conditions that an equivalence relation does not only allow the formation of a quotient algebra, but that this quotient is also again a pseudo weak effect algebra.

Last, we show that pseudo BL-effect algebras are subdirect products of linearly ordered ones.


Pseudo weak effect algebra Pseudo weak difference poset Ideal Congruence Subdirect product 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.College of Mathematic and Information ScienceShaanxi Normal UniversityXi’anChina
  2. 2.College of Computer ScienceShaanxi Normal UniversityXi’anChina

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