Characterization of some special rings via Linkage

Document Type : Research Paper


1 Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran

2 Faculty of Mathematical sciences and computer, Kharazmi university, Tehran, Iran


Providing a description of linked ideals in a commutative Noetherian ring in terms of some associated prime ideals, we make a characterization of Cohen-Macaulay, Gorenstein and regular local rings in terms of their linked ideals. More precisely, it is shown that the local ring $(R,\fm)$ is Cohen-Macaulay if and only if any linked ideal is unmixed. Also, $(R,\fm)$ is Gorenstein if and only if
any unmixed ideal $\fa$ is linked by every maximal regular sequence in $\fa$.
We also compute the annihilator of top local cohomology modules in some special cases.