Lexicographic Effect Algebras
Anatolij Dvure\v{c}enskij

TL;DR
This paper explores a class of effect algebras represented as lexicographic products of po-groups, establishing algebraic conditions, categorical equivalences, and representation theorems including subdirect product representations.
Contribution
It introduces the category of strong (H,u)-perfect effect algebras and proves its categorical equivalence to directed po-groups with interpolation, advancing the structural understanding of effect algebras.
Findings
Characterization of effect algebras as lexicographic products
Categorical equivalence between strong (H,u)-perfect effect algebras and directed po-groups
Representation theorems including subdirect product representations
Abstract
In the paper we investigate a class of effect algebras which can be represented in the form of the lexicographic product , where is an Abelian unital po-group and is an Abelian directed po-group. We study algebraic conditions when an effect algebra is of this form. Fixing a unital po-group , the category of strong -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.
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Taxonomy
TopicsAdvanced Algebra and Logic · Fuzzy and Soft Set Theory · Logic, Reasoning, and Knowledge
