• Journal of the Korean Mathematical Society
• /
• v.59 no.2
• /
• pp.379-405
• /
• 2022

We introduce the notions of Koszul N-complex, Čech N-complex and telescope N-complex, explicit derived torsion and derived completion functors in the derived category D_N (R) of N-complexes using the Čech N-complex and the telescope N-complex. Moreover, we give an equivalence between the categories of cohomologically 𝖆-torsion N-complexes and cohomologically 𝖆-adic complete N-complexes, and prove that over a commutative Noetherian ring, via Koszul cohomology, via RHom cohomology (resp. ⊗ cohomology) and via local cohomology (resp. derived completion), all yield the same invariant.

• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.3
• /
• pp.197-204
• /
• 2022

In this article, we define a modified Koszul complex, which we call a quantized Koszul complex, on a quantum space ring, and we also prove that it is an acyclic complex.

• Honam Mathematical Journal
• /
• v.10 no.1
• /
• pp.31-46
• /
• 1988

• Journal of the Korean Mathematical Society
• /
• v.49 no.5
• /
• pp.1083-1096
• /
• 2012

For a given ideal I of a Noetherian ring R and an arbitrary integer ${\kappa}{\geq}-1$, we apply the concept of ${\kappa}$-regular sequences and the notion of ${\kappa}$-depth to give some results on modules called ${\kappa}$-Cohen Macaulay modules, which in local case, is exactly the ${\kappa}$-modules (as a generalization of f-modules). Meanwhile, we give an expression of local cohomology with respect to any ${\kappa}$-regular sequence in I, in a particular case. We prove that the dimension of homology modules of the Koszul complex with respect to any ${\kappa}$-regular sequence is at most ${\kappa}$. Therefore homology modules of the Koszul complex with respect to any filter regular sequence has finite length.

• Bulletin of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.265-275
• /
• 1992

The characteristic free representation theory of the general linear group has found a wide range of applications, ranging from the theory of free resolutions to the symmetric function theory. Representation theory is used to facilitate the calculation of explicit free resolutions of large classes of ideals (and modules). Recently, K. Akin and D. A. Buchsbaum [2] realized the Jacobi-Trudi identity for a Schur function as a resolution of GL$_{n}$-modules. Over a field of characteristic zero, it was observed by A. Lascoux [6]. T.Jozefiak and J.Weyman [5] used the Koszul complex to realize a formula of D.E. Littlewood as a resolution of schur modules. This leads us to further study resolutions of Schur modules of a particular form. In this article we will describe some new classes of finite free resolutions associated to the Pieri type skew Young diagrams. As a special case of these finite free resolutions we obtain the generalized Koszul complex constructed in [1]. In section 2 we review some of the basic difinitions and properties of Schur modules that we shall use. In section 3 we describe certain exact complexes associated to the Pieri type skew partitions. Throughout this article, unless otherwise specified, R is a commutative ring with an identity element and a mudule F is a finitely generated free R-module.e.