
TL;DR
This paper introduces rooted tree modules over certain algebras, providing combinatorial criteria for indecomposability and methods for their decomposition and recursive construction.
Contribution
It offers a combinatorial characterization of indecomposability and iterative methods for decomposing and constructing rooted tree modules over zero-relation algebras.
Findings
Characterization of indecomposability via quiver morphisms
Iterative method for decomposing RTMs
Recursive construction of indecomposable RTMs
Abstract
A rooted tree module (RTM) over a zero-relation algebra over a field is given by the data of a quiver morphism from a rooted tree (either with a source or a sink) taking paths in to paths in not lying in . When , we provide a checkable combinatorial characterization of the indecomposability of the RTM in terms of non-existence of idempotent quiver morphisms satisfying and . Further, we provide an iterative method to decompose an RTM into indecomposable RTMs as well as a method to recursively construct indecomposable RTMs.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Commutative Algebra and Its Applications
