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Weak Resolution Dimensions of Subcategories
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AI
DOI：10.3390/axioms14110824.png)
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Abstract
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We investigate the relationships between the weak resolution dimensions of subcategories of module categories of Artinian algebras in the present paper. Let Lambda be an Artinian algebra, and A, B and X subcategories of Lambda-modules, such that each object X in X is given by an exact sequence 0 -> A -> B -> X -> 0 with A is an element of ObA and B is an element of ObB. We prove that the weak resolution dimension of X is bounded above by the sum of the corresponding dimensions for A and B plus 1. As applications, we study weak resolution dimensions of Artinian algebras under left idealized extensions and conditions on special ideals.
Keywords:
weak resolution dimension
left idealized extension
subcategory
Journal
A
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1.6
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484
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4.4K