caa a22 4500 606161252 CHVBK 20210128100633.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10468-014-9504-9 doi (NATIONALLICENCE)springer-10.1007/s10468-014-9504-9 The ϕ -Dimension: A New Homological Measure [Elektronische Daten] [Sônia Fernandes, Marcelo Lanzilotta, Octavio Mendoza Hernández] 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 Ext A i ( − , − ) $\text{Ext}^{i}_{A}(-, -)$ and in terms of Tor's bi-functors Tor i A ( − , − ) . $\text{Tor}^{A}_{i}(-,-).$ 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. Springer Science+Business Media Dordrecht, 2014 Finitistic dimension nationallicence Igusa-Todorov functions nationallicence Derived categories nationallicence Fernandes Sônia Departamento de Matemática, Universidade Federal de Viçosa, CP 36570000, Viçosa, MG, Brasil aut Lanzilotta Marcelo Instituto de Matemática y Estadística Rafael Laguardia, Facultad de Ingeniería, Universidad de la República, J. Herrera y Reissig 565, CP 11300, Montevideo, Uruguay aut Mendoza Hernández Octavio Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, C.P. 04510, México, D.F., México aut Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 463-476 1386-923X 18:2<463 2015 18 10468 https://doi.org/10.1007/s10468-014-9504-9 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-014-9504-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Fernandes Sônia Departamento de Matemática, Universidade Federal de Viçosa, CP 36570000, Viçosa, MG, Brasil aut NATIONALLICENCE 700 1- Lanzilotta Marcelo Instituto de Matemática y Estadística Rafael Laguardia, Facultad de Ingeniería, Universidad de la República, J. Herrera y Reissig 565, CP 11300, Montevideo, Uruguay aut NATIONALLICENCE 700 1- Mendoza Hernández Octavio Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, C.P. 04510, México, D.F., México aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 463-476 1386-923X 18:2<463 2015 18 10468