• Title, Summary, Keyword: Koszul complex

Search Result 4, Processing Time 0.025 seconds

ON THE κ-REGULAR SEQUENCES AND THE GENERALIZATION OF F-MODULES

  • Ahmadi-Amoli, Khadijeh;Sanaei, Navid
    • 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.

Certain exact complexes associated to the pieri type skew young diagrams

  • Chun, Yoo-Bong;Ko, Hyoung J.
    • 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.

  • PDF

A NOTE ON THE LOCAL HOMOLOGY

  • Rasoulyar, S.
    • Bulletin of the Korean Mathematical Society
    • /
    • v.41 no.2
    • /
    • pp.387-391
    • /
    • 2004
  • Let A be Noetherian ring, a= (${\tau}_1..., \tau_n$ an ideal of A and $C_{A}$ be category of A-modules and A-homomorphisms. We show that the connected left sequences of covariant functors ${limH_i(K.(t^t,-))}_{i\geq0}$ and ${lim{{Tor^A}_i}(\frac{A}{a^f}-)}_{i\geq0}$ are isomorphic from $C_A$ to itself, where $\tau^t\;=\;{{\tau_^t}_1$, ㆍㆍㆍ${\tau^t}_n$.

MIXED MULTIPLICITIES OF MAXIMAL DEGREES

  • Thanh, Truong Thi Hong;Viet, Duong Quoc
    • Journal of the Korean Mathematical Society
    • /
    • v.55 no.3
    • /
    • pp.605-622
    • /
    • 2018
  • The original mixed multiplicity theory considered the class of mixed multiplicities concerning the terms of highest total degree in the Hilbert polynomial. This paper defines a broader class of mixed multiplicities that concern the maximal terms in this polynomial, and gives many results, which are not only general but also more natural than many results in the original mixed multiplicity theory.