Showing papers by "Thomas Vetterlein published in 2001"

Pseudoeffect Algebras. I. Basic Properties

Abstract: As a noncommutative generalization of effect algebras, we introduce pseudoeffect algebras and list some of their basic properties. For the purpose of a structure theory, we further define several kinds of Riesz-like properties for pseudoeffect algebras and show how they are interrelated.

Pseudoeffect Algebras. II. Group Representations

Abstract: This paper is the continuation of the previous paper by Dvurecenskij and Vetterlein (2001), Int J Theor Phys 40(3) We show that any pseudoeffect algebra fulfilling a certain property of Riesz type is representable by a unit interval of some (not necessarily Abelian) partially ordered group The relation of pseudoeffect to pseudo-MV algebras is made clear, and the &ell-group representation theorem for the latter structure is re-proved

Congruences and States on Pseudoeffect Algebras

Abstract: We study congruences on pseudoeffect algebras, which were recently introduced as a non-commutative generalization of effect algebras. We introduce ideals for these algebras and give a sufficient condition for an ideal to determine a congruence. Furthermore, states on pseudoeffect algebras are considered. It is shown that any interval pseudoeffect algebra maps homomorphically into an effect algebra whose states are in a one-to-one correspondence to the states of the original algebra.

Generalized Pseudo-Effect Algebras

Abstract: We introduce generalized pseudo-effect algebras as a non-commutative version of generalized effect algebras.