2015/03/23 by Freitas, T. H., Pérez, V. H. Jorge
#13D45 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1503.06784
Let (R,\mathfrakm) be a commutative Noetherian local ring, M be a finitely generated R-module and \mathfraka, I and J be ideals of R. We investigate the structure of formal local cohomology modules of \mathfrakFi_\mathfraka,I,J(M) and \check\mathfrakFi_\mathfraka,I,J(M) with respect to a pair of ideals, for all i≥ 0. The main subject of the paper is to study the finiteness properties and Artinianness of \mathfrakFi_\mathfraka,I,J(M) and \check\mathfrakFi_\mathfraka,\mathfrakm,J(M). We study the maximum and minimum integer i∈ \N such that \mathfrakFi_\mathfraka,\mathfrakm,J(M) and \check\mathfrakFi_\mathfraka,\mathfrakm,J(M) are not Artinian. We obtain some results involving cossuport, coassociated and attached primes for formal local cohomology modules with respect to a pair of ideals. Also, we give an criterion involving the concepts of finiteness and vanishing of formal local cohomology modules and Čech-formal local cohomology modules with respect to a pair of ideals.