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.
Jahangiri, M. and Sayyari, K. (2020). Characterization of some special rings via Linkage. Journal of Algebra and Related Topics, 8(1), 67-81. doi: 10.22124/jart.2020.15507.1186
MLA
Jahangiri, M. , and Sayyari, K. . "Characterization of some special rings via Linkage", Journal of Algebra and Related Topics, 8, 1, 2020, 67-81. doi: 10.22124/jart.2020.15507.1186
HARVARD
Jahangiri, M., Sayyari, K. (2020). 'Characterization of some special rings via Linkage', Journal of Algebra and Related Topics, 8(1), pp. 67-81. doi: 10.22124/jart.2020.15507.1186
CHICAGO
M. Jahangiri and K. Sayyari, "Characterization of some special rings via Linkage," Journal of Algebra and Related Topics, 8 1 (2020): 67-81, doi: 10.22124/jart.2020.15507.1186
VANCOUVER
Jahangiri, M., Sayyari, K. Characterization of some special rings via Linkage. Journal of Algebra and Related Topics, 2020; 8(1): 67-81. doi: 10.22124/jart.2020.15507.1186
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