On irreducibility of monomial 7 × 7−matrix over local ring

Irreducibility testing over local fields

The purpose of this paper is to describe a method to determine whether a bivariate polynomial with rational coefficients is irreducible when regarded as an element in Q((x))[y], the ring of polynomials with coefficients from the field of Laurent series in x with rational coefficients. This is achieved by computing certain associated Puiseux expansions, and as a result, a polynomial-time complex...

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

2 7 Ja n 20 00 Cohomology On Toric Varieties and Local Cohomology With Monomial Supports

In this note we describe aspects of the cohomology of coherent sheaves on a complete toric variety X over a field k and, more generally, the local cohomology, with supports in a monomial ideal, of a finitely generated module over a polynomial ring S. This leads to an efficient way of computing such cohomology, for which we give explicit algorithms. The problem is finiteness. The i local cohomol...

Local Cohomology at Monomial Ideals

On Skew Cyclic Codes over a Finite Ring

In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.