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https://locus.ufv.br//handle/123456789/23550
Tipo: | Artigo |
Título: | The ϕ-Dimension: A new homological measure |
Autor(es): | Fernandes, Sônia Maria Lanzilotta, Marcelo Hernández, Octavio Mendoza |
Abstract: | In Igusa and Todorov (2005) introduced two functions ϕ and ψ, which are natural and important homological measures generalising the notion of the projective dimension. These Igusa-Todorov functions have become a powerful tool to understand better the finitistic dimension conjecture. In this paper, for an artin R-algebra A and the Igusa-Todorov function ϕ, we characterise the ϕ-dimension of A in terms of the bi-functors ExtiA(−,−)ExtAi(−,−) and in terms of Tor’s bi-functors TorAi(−,−).ToriA(−,−). Furthermore, by using the first characterisation of the ϕ-dimension, we show that the finiteness of the ϕ-dimension of an artin algebra is invariant under derived equivalences. As an application of this result, we generalise the classical Bongartz’s result (Bongartz, Lect. Notes Math. 903, 26–38, (1981), Corollary 1) as follows: For an artin algebra A, a tilting A-module T and the endomorphism algebra B = End A (T) o p , we have that ϕ dim (A) − pd T ≤ ϕ dim (B) ≤ ϕ dim (A) + pd T. |
Palavras-chave: | Finitistic dimension Igusa-Todorov functions Derived categories |
Editor: | Algebras and Representation Theory |
Tipo de Acesso: | Springer Science+Business Media Dordrecht |
URI: | https://doi.org/10.1007/s10468-014-9504-9 http://www.locus.ufv.br/handle/123456789/23550 |
Data do documento: | Abr-2015 |
Aparece nas coleções: | Artigos |
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artigo.pdf Until 2100-12-31 | Texto completo | 366,37 kB | Adobe PDF | Visualizar/Abrir ACESSO RESTRITO |
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