Reversible AJW-algebras
Shavkat Ayupov, Farhodjon Arzikulov

TL;DR
This paper proves that special AJW-algebras can be decomposed into parts that are reversible or totally nonreversible, providing a structural classification based on central projections.
Contribution
It introduces a decomposition of special AJW-algebras into reversible and nonreversible components using central projections.
Findings
Existence of central projections dividing the algebra into three parts.
Characterization of reversible parts via ideals and duals.
Identification of a totally nonreversible component.
Abstract
In this article it is proved that for every special AJW-algebra there exist central projections , , , such that (1) is reversible and there exists a norm-closed two sided ideal of such that ; (2) is reversible and ; (3) is a totally nonreversible AJW-algebra.
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Taxonomy
TopicsAdvanced Algebra and Logic · Logic, Reasoning, and Knowledge · Rough Sets and Fuzzy Logic
