The Kuroš-Ore property, replaceable irredundant decompositions

Andrzej Walendziak

AI-generated Abstract

This paper generalizes a classical result regarding the Kuroš-Ore property in semimodular algebraic lattices satisfying the descending chain condition. It establishes that such lattices exhibit the Kuroš-Ore property if and only if they possess replaceable irredundant decompositions. Also discussed are foundational concepts of lattice theory, proof of related lemmas, and examples to illustrate the necessity of semimodularity for the Kuroš-Ore property.

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