Support $τ$-tilting modules over one-point extensions

Abstract

Let B be the one-point extension algebra of A by an A-module X. We proved that every support τ -tilting A-module can be extended to be a support τ -tilting B-module by two different ways. As a consequence, it is shown that there is an inequality | sτ -tilt B| 2| sτ -tilt A|.