caa a22 4500 605461775 CHVBK 20210128100245.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10114-015-3623-z doi (NATIONALLICENCE)springer-10.1007/s10114-015-3623-z Shi Hong Department of Mathematics, Nanjing University of Finance and Economics, 210046, Nanjing, P. R. China aut Homological dimensions of the extension algebras of monomial algebras [Elektronische Daten] [Hong Shi] The main objective of this paper is to study the dimension trees and further the homological dimensions of the extension algebras — dual and trivially twisted extensions — with a unified combinatorial approach using the two combinatorial algorithms — Topdown and Bottomup. We first present a more complete and clearer picture of a dimension tree, with which we are then able, on the one hand, to sharpen some results obtained before and furthermore reveal a few more hidden subtle homological phenomenons of or connections between the involved algebras; on the other hand, to provide two more efficient combinatorial algorithms for computing dimension trees, and consequently the homological dimensions as an application. We believe that the more refined complete structural information on dimension trees will be useful to study other homological properties of this class of extension algebras. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Topdown nationallicence bottomup nationallicence dimension tree nationallicence syzygy nationallicence finitistic dimensions nationallicence Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/4(2015-04-01), 675-694 1439-8516 31:4<675 2015 31 10114 https://doi.org/10.1007/s10114-015-3623-z 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/s10114-015-3623-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Shi Hong Department of Mathematics, Nanjing University of Finance and Economics, 210046, Nanjing, P. R. China aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/4(2015-04-01), 675-694 1439-8516 31:4<675 2015 31 10114