Finiteness of Composed local cohomology modules
Fatemeh Dehghani-Zadeh
TL;DR
This paper investigates the finiteness and Artinianness properties of generalized local cohomology modules, providing new insights into their structure under specific conditions and ideal properties.
Contribution
It establishes conditions for the cofiniteness and Artinianness of generalized local cohomology modules, extending understanding of their finiteness properties in algebraic settings.
Findings
Cofiniteness of generalized local cohomology modules is characterized under certain conditions.
Artinianness of specific local cohomology modules is proven in graded contexts.
Results connect ideal properties with the finiteness and Artinianness of modules.
Abstract
Cofiniteness of the generalized local cohomology modules Hai(M, N) of two R-modules M and N with respect to an ideal a is studied for some i,s with a specified property. Furthermore, Artinianness of Hbj 0(Hai(M, N)) is investigated by using the above result, in certain graded situations, where b 0 is an ideal of R 0 such that b 0 + a 0 is an m 0-primary ideal.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic structures and combinatorial models