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Dvurečenskij, Anatolij; Vetterlein, Thomas

doi:10.1023/a:1015561420306

Foundations of Physics Letters

2001

DOI: 10.1023/a:1015561420306

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Anatolij Dvurečenskij

Thomas Vetterlein

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Cited by 30 publications

References 17 publications

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Archimedeanness and the MacNeille completion of pseudoeffect algebras and po-groups

Dvurečenskij

Vetterlein

2003

Algebra Universalis

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Pseudoeffect (PE-) algebras are partial algebras differing from effect algebras in that they need not satisfy the commutativity assumption. PE-algebras typically arise from intervals of po-groups; this applies in particular to all those which satisfy a certain Riesz property.In this paper, we discuss the property of archimedeanness for PE-algebras on the one hand and for po-groups on the other hand. We prove that under the assumption of suphomogeneity, archimedeanness holds for a PE-algebra with the Riesz property if and only if it holds for its representing group. The algebra is in that case commutative. This result is established by using the technique of MacNeille completion. We give the exact condition for this completion to exist, and we clearly exhibit the role played by archimedeanness and by sup-homogeneity.

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Archimedeanness and the MacNeille completion of pseudoeffect algebras and po-groups

Dvurečenskij

Vetterlein

2003

Algebra Universalis

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Lexicographic effect algebras

Dvurečenskij

2016

Algebra Univers.

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In the paper we investigate a class of effect algebras which can be represented in the form of the lexicographic product Γ(H − → × G, (u, 0)), where (H, u) is an Abelian unital po-group and G is an Abelian directed po-group. We study algebraic conditions when an effect algebra is of this form. Fixing a unital po-group (H, u), the category of strong (H, u)-perfect effect algebra is introduced and it is shown that it is categorically equivalent to the category of directed po-group with interpolation. We show some representation theorems including a subdirect product representation by antilattice lexicographic effect algebras. 1

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Generalized Ideals and Supports in Pseudo Effect Algebras

Shang¹,

2006

Soft Comput

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In this paper we introduce the definitions of generalized ideals and generalized filters in pseudo effect algebras. From the generalized ideals (filters), we obtain some equivalent characterization of ideals (filters). The relationships among generalized ideals, ideals and local ideals are studied in detail. We also establish an isomorphism between the set of supports and the set of generalized ideals of pseudo effect algebras.

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Cited by 30 publications

References 17 publications

Archimedeanness and the MacNeille completion of pseudoeffect algebras and po-groups

Archimedeanness and the MacNeille completion of pseudoeffect algebras and po-groups

Lexicographic effect algebras

Generalized Ideals and Supports in Pseudo Effect Algebras

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