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A Note on Artinianess of Certain Generalized | ||
| Journal of Sciences, Islamic Republic of Iran | ||
| مقاله 8، دوره 19، شماره 3، آذر 2008 اصل مقاله (205.35 K) | ||
| چکیده | ||
| Let ?: R0?R be a ring homomorphism and suppose that a and a0, respectively, are ideals of R and R0 such that is an Artinian ring. Let M and N be two finitely generated R-modules and suppose that (R0,m0) is a local ring. In this note we prove that the R-modules and are Artinian for all integers i and j, whenever and . Also we will show that if a is principal, then the R-modules and are Artinian, for all integers i and j. Moreover, we will show that if is the largest integer i such that is not Artinian, then the R-modules and are Artinian, for and all . Also as a consequence of this result we get that the R-modules and are artinian, for j=d, d?1, in which is the cohomological dimension of M and N with respect to a. Our results recover the corresponding known ones. | ||
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