Abstract
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.
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