where the map R/(x1 , . . . , x m n ) −→ R/(x m+1 1 , . . . , x m+1 n ) is multiplication by the image of the element x1 · · ·xn. As these descriptions suggest, H a(R) is usually not finitely generated as an R-module. However local cohomology modules have useful finiteness properties in certain cases, e.g., for a local ring (R,m), the modules H m(R) satisfy the descending chain condition. This ...

After recalling the definition of codes as modules over skew polynomial rings, whose multiplication is defined by using an automorphism and a derivation, and some basic facts about them, in the first part of this paper we study some of their main algebraic and geometric properties. Finally, for module skew codes constructed only with an automorphism, we give some BCH type lower bounds for their...

Poirier and Reutenauer defined a Hopf algebra on the Z-span of all standard Young tableaux in [10], which is later studied in [4, 11]. The Robinson-Schensted-Knuth insertion was used to relate the bialgebra to Schur functions. Schur function is a class of symmetric functions that can be determined by the summation of all semistandard Young tableaux of shape . With the help of the PR-bialgebra, ...

A divisibility test of Arend Heyting, for polynomials over a …eld in an intuitionistic setting, may be thought of as a kind of division algorithm. We show that such a division algorithm holds for divisibility by polynomials of content 1 over any commutative ring in which nilpotent elements are zero. In addition, for an arbitary commutative ring R, we characterize those polynomials g such that t...

In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach ...

For any abelian group G and any function f : G → G we define a commutative binary operation or “multiplication” on G in terms of f . We give necessary and sufficient conditions on f for G to extend to a commutative ring with the new multiplication. In the case where G is an elementary abelian p-group of odd order, we classify those functions which extend G to a ring and show, under an equivalen...

The switch control unit module is a critical core control module of the all-electronic computer interlocking system. Switch in the wrong place as the top event, use the Relex software for quantitative analysis of the importance of analysis method and found a key part of the module designs. The weak link in the system design through the use of the ‘2-Vote-2’ modular architecture analysis showed ...

We prove that the local height of a point on a Drinfeld module can be computed by averaging the logarithm of the distance to that point over the torsion points of the module. This gives rise to a Drinfeld module analog of a weak version of Siegel’s integral points theorem over number fields and to an analog of a theorem of Schinzel’s regarding the order of a point modulo certain primes.

Sparse matrix-vector multiplication is the kernel for many scientiic computations. Parallelizing this operation requires the matrix to be divided among processors. This division is commonly phrased in terms of graph partitioning. Although this abstraction has proved to be very useful, it has signiicant aws and limitations. The cost model implicit in this abstraction is only a weak approximation...