Igusa-Todorov Functions And Finitistic Dimension Conjecture

For an Artin algebra A,the finitistic dimension conjecture says that the supremum of the projective dimension of all finitely generated A-modules of finite projective dimension is finite.During the research on this conjecture,Igusa-Todorov [16] functions demonstrated their powerfulness in estimating the bounds of projective dimensions of modules.We will review the concepts and properties of Igusa-Todorov functions,as well as new notions and methods derived from them.In particular,the class of IgusaTodorov algebras defined by Wei [24] contains many other algebras of finite finitistic dimension.We will give a negative answer to Wei’s question whether all Artin algebras are Igusa-Todorov algebras.