Cohen–Macaulay Modules in Dimension >s and Results on Local Cohomology

Let (R,𝔪) be a local ring and s ≥ ?1. Using the notion of M-sequence in dimension > s, we introduce Cohen–Macaulay modules in dimension > s. Among other things concerning Cohen–Macaulay modules in dimension > s, some finiteness results of the support and the associated primes of local cohomology modules are investigated.     

On Fiber Coefficients of Fiber Cones †

Let (R,𝔪) be a Cohen–Macaulay local ring of dimension d > 0, I an 𝔪-primary ideal of R, and K an ideal containing I. When depth G(I) ≥ d ? 1, depth F_K(I) ≥ d ? 2, and r(I|K) < ∞, we calculate the fiber coefficients f_i(I). Under the above assumptions on depth G(I) and r(I|K), we give an upper bound for f₁(I), and also provide a characterization, in terms of f₁(I), of the condition depth F_K(I) ≥ d ? 2.     

A Lower Bound on the Second Fiber Coefficient of the Fiber Cones

Let (R, 𝔪) be a Cohen–Macaulay local ring of dimension d > 0, I an 𝔪-primary ideal of R and K an ideal containing I. When depth G(I) ≥ d ? 1 and r(I | K) < ∞, we present a lower bound on the second fiber coefficient of the fiber cones, and also provide a characterization, in terms of f ₂(I, K), of the condition depth F _K (I) ≥ d ? 1.     

Central Units,Class Sums and Characters of the Symmetric Group

In the search for central units of a group algebra, we look at the class sums of the group algebra of the symmetric group S _n in characteristic zero, and we show that they are units in very special instances.     

Almost Split Sequences in Dimension One

Let R be a complete discrete valuation ring with quotient field K, and let Λ be an R-order in a semisimple K-algebra. For an indecomposable Λ-lattice E, a sublattice Bi E satisfying Rad E ? Bi E is defined, and it is shown that the middle term H of an almost split sequence τE ? H ? E can be obtained by an amalgamation of E/Bi E with E′/τE for a suitable overlattice E′ of τE. The method is bound to dim R = 1.     

关于代换系统拓扑序列熵的注记

Goodman证明了对两符号等长代换系统, 如果代换规则中0和1对应的词只有一个位置不同,那么对应的代换系统为null的, 即此系统沿着任意正整数序列的序列熵均为0. 在本文中, 我们针对系统的结构特征, 通过考察因子系统, 给出了此经典结果的另外一种证明. 同时, 对此类代换系统沿着给定序列的复杂性, 我们得到了比Goodman更为精确的估计.