CONSTRUCTING NONPROXY SMALL TEST MODULES FOR THE COMPLETE INTERSECTION PROPERTY

Abstract A local ring R is regular if and only every finitely generated -module has finite projective dimension. Moreover, the residue field k a test module: This characterization can be extended to bounded derived category $\mathsf {D}^{\mathsf f}(R)$ , which contains small objects regular. Recent results of Pollitz, completing work initiated by Dwyer–Greenlees–Iyengar, yield an analogous for complete intersections: intersection object in proxy small. In this paper, we study return world -modules, search -modules that are not whenever intersection. We give algorithm construct such modules certain settings, including over equipresented rings Stanley–Reisner rings.