Constacyclic codes may naturally be viewed as objects arising from the cohomological concept of a cocycle. Cohomology theory suggests a transformation which is used to show, under certain circumstances, a cyclic code of length mn over a ring R is isomorphic to the direct sum of m constacyclic codes of length n. In particular this isomorphism holds in many local rings (for example Galois rings) ...

Let V be an absolutely irreducible representation of a profinite group G over the residue field k of a noetherian local ring O. For local complete O-algebras A with residue field k the representations of G over A that reduce to V over k are given by O-algebra homomorphisms R → A, where R is the universal deformation ring of V . We show this with an explicit construction of R. The ring R is noet...

‎Let $I$ denote an ideal of a Noetherian ring $R$‎. ‎The purpose of‎ ‎this article is to introduce the concepts of quintasymptotic‎ ‎sequences over $I$ and quintasymptotic cograde of $I$‎, ‎and to show that they play a role analogous to quintessential sequences‎ ‎over $I$ and quintessential cograde of $I$‎. ‎We show that‎, ‎if $R$ is‎ ‎local‎, ‎then the quintasymptotic cograde of $I$ is una...

This paper introduces an approach to the axiomatic theory of quadratic forms based on {tmem{presentable}} partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of {tmem{quadratically p...

let $r$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎a right $r$-module $m$ is called $(n‎, ‎d)$-projective if $ext^{d+1}_r(m‎, ‎a)=0$ for every $n$-copresented right $r$-module $a$‎. ‎$r$ is called right $n$-cocoherent if every $n$-copresented right $r$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $r$-module is $(n‎, ‎d)$-projective‎. ‎$r$ ...

We prove that the universal unramified deformation ring R of a continuous Galois representation ρ : GF+ → GLn(k) (for a totally real field F and finite field k) is finite over O = W (k) in many cases. We also prove (under similar hypotheses) that the universal deformation ring R is finite over the local deformation ring R.

Ring-diagram analysis is a technique of local helioseismology used to infer plasma flows in the solar convection zone which generates intermediate data products known as ring-fitting parameters. Knowing the sensitivity of ringfitting parameters to actual flows in the Sun is important for interpreting these measurements.Working in plane-parallel geometry, we compute the linear sensitivity of rin...

Let (R, m) be a local commutative ring. Suppose that m is principal and that m = 0. We give a complete description of the cellular lattice of perfect chain complexes of modules over this ring.

The purpose of this article is to prove that Gersten’s conjecture for a commutative discrete valuation ring is true. Combining with the result of [GL87], we learn that Gersten’s conjecture is true if the ring is a commutative regular local, smooth over a commutative discrete valuation ring.