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., & 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
M. Jahangiri; Kh. 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
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
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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