Abstract
The notion of SGCM ideals is introduced as an extension of the known notion of SCM ideals. Some properties of SGCM ideals, which are closely related to SCM ideals in a Gorenstein local ring, are given. It turns out that the SGCM property is retained through the even linkage class in a Gorenstein local ring. Also, we establish the equality of the finiteness dimension of the residue class rings of two evenly linked ideals. Finally, some slight relations between SGCM ideals and CM d-sequences are obtained.
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