In the mid-1960s Borevič and Faddeev initiated the study of the Galois module structure of groups of pth-power classes of cyclic extensions K/F of pth-power degree. They determined the structure of these modules in the case when F is a local field. In this paper we determine these Galois modules for all base fields F .

It is shown that the automorphism group of the shorter Moonshine module constructed in [Höh95] (also called Baby Monster vertex operator superalgebra) is the direct product of the finite simple group known as the Baby Monster and the cyclic group of order 2.

For a prime number p, we construct a generating set for the ring of invariants for the p+1 dimensional indecomposable modular representation of a cyclic group of order p. We then use the constructed invariants to describe the decomposition of the symmetric algebra as a module over the group ring, confirming the Periodicity Conjecture of Ian Hughes and Gregor Kemper for this case.

It is shown that a ring R is (von Neumann) regular if and only if every cyclic left R-module is GP -injective if and only if R is left PP and left GP -injective. In addition, two examples are given to answer two open questions in the negative. 2000 Mathematics Subject Classification: 16E50, 16D60

The construction of cyclic codes can be generalized to so-called ”module θ-codes” using noncommutative polynomials. The product of the generator polynomial g of a self-dual ”module θ-code” and its ”skew reciprocal polynomial” is known to be a noncommutative polynomial of the form X − a, reducing the problem of the computation of all such codes to the resolution of a polynomial system where the ...

We prove that the Scott module whose vertex is isomorphic to a direct product of generalized quaternion $2$-group and cyclic Brauer indecomposable. This result generalizes similar results which are obtained for abelian, dihedral, quaternion, semidihedral wreathed vertices.

We study the H n ( 0 ) -module S ? ? due to Tewari and van Willigenburg, which was constructed using new combinatorial objects called standard permuted composition tableaux decomposed into cyclic submodules. First, we show that every direct summand appearing in their decomposition is indecomposable characterize when indecomposable. Second, find characteristic relations among 's expand image of ...

Given a knot K in S 3 and a positive integer p, there is a unique p-fold cyclic connected cover X v --, S 3 K, and this can be completed to a branched cover M e --* S 3. When p is prime, the homology group H1 (M e) is torsion and was one of the earliest knot invariants (predating the Alexander polynomial). It was used by Alexander and Briggs [A-B] to distinguish knots up to 8 crossings and all ...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

a module $m$ is called $emph{h}$-cofinitely supplemented if for every cofinite submodule $e$ (i.e. $m/e$ is finitely generated) of $m$ there exists a direct summand $d$ of $m$ such that $m = e + x$ holds if and only if $m = d + x$, for every submodule $x$ of $m$. in this paper we study factors, direct summands and direct sums of $emph{h}$-cofinitely supplemented modules. let $m$ be an $emph{h}$...