Title of article :
Burch Index, Summands of Syzygies and Linearity in Resolutions
Author/Authors :
Dao ، Hailong Department of Mathematics - Faculty of Science - University of Kansas , Eisenbud ، David Department of Mathematics - Faculty of Science, Berkeley and the Mathematical Sciences Research Institute - University of California
Abstract :
The Burch index is a new invariant of a local ring R whose positivity implies a kind of linearity in resolutions of R-modules. We show that if R has depth zero and Burch index at least 2, then any non-free 7th R-syzygy contains the residue field as a direct summand. We compute the Burch index in various cases of interest.
Keywords :
Burch rings , Burch index , Free resolutions , Linearity of syzygies , Summands of syzygies ,
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
