Bi-amalgamations subject to the arithmetical property
S. Kabbaj, N. Mahdou, M. A. S. Moutui
TL;DR
This paper characterizes when bi-amalgamations inherit the arithmetical property, providing new conditions and applications to weak global dimension and semihereditary property transfer, supported by illustrative examples.
Contribution
It introduces necessary and sufficient conditions for bi-amalgamations to be arithmetical, advancing previous work with new results and examples.
Findings
Bi-amalgamations inherit arithmetical property under specific conditions.
Applications to weak global dimension and semihereditary property transfer.
New illustrative examples of bi-amalgamations.
Abstract
This paper establishes necessary and sufficient conditions for a bi-amalgamation to inherit the arithmetical property, with applications on the weak global dimension and transfer of the semihereditary property. The new results compare to previous works carried on various settings of duplications and amalgamations, and capitalize on recent results on bi-amalgamations. All results are backed with new and illustrative examples arising as bi-amalgamations.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology