Algorithms to decide isomorphism of modules have been honed continually over the last 30 years, and their range of applicability has been extended to include modules over a wide range of rings. Highly efficient computer implementations of these algorithms form the bedrock of systems such as GAP and Magma, at least in regard to computations with groups and algebras. By contrast, the fundamental ...

We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic coh...

Given an oriented knot K in S and a TQFT, Turaev and Viro defined modules somewhat analogous to the Alexander module. We work with the (Vp, Zp) theories of Blanchet, Habegger, Masbaum and Vogel [BHMV] for p ≥ 3, and consider the associated modules. In [G], we defined modules which also depend on the extra data of a color c which is assigned to a meridian of the knot in the construction of the m...

Interest in the application of computer simulation in construction has been growing since the introduction of the CYCLONE (CYCLic Operation NEtwork) methodology in 1973. The CYCLONE methodology has become well established and its six standard modeling elements provide a simple, straightforward tool for the study of various construction operations. Many construction-specific simulation systems e...

Two theorems about the vertices of indecomposable Specht modules for the symmetric group, defined over a field of prime characteristic p, are proved: 1. The indecomposable Specht module S has non-trivial cyclic vertex if and only if λ has p-weight 1. 2. If p does not divide n and S(n−r,1 ) is indecomposable then its vertex is a p-Sylow subgroup of Sn−r−1 × Sr. Mathematics Subject Classification...

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

For an odd prime number p, we study the of generators unramified Iwasawa modules maximal multiple ℤ p -extensions over algebra. In our previous paper, under several assumptions for imaginary quadratic field, obtained a necessary and sufficient condition cyclicity module The present work provides computational methods numerical examples that are cyclic as We remark do not require assumption Gree...

In this paper we study the module contractibility ofBanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. Also weinvestigate module contractibility of Banach algebras with theconcept of the module diagonal.

Given a ring of ternions R, i. e., a ring isomorphic to that of upper triangular 2×2 matrices with entries from an arbitrary commutative field F , a complete classification is performed of the vectors from the free left R-module R, n ≥ 1, and of the cyclic submodules generated by these vectors. The vectors fall into 5 + |F | and the submodules into 6 distinct orbits under the action of the gene...

Natural or synthetic cyclic peptides often possess pronounced bioactivity. Their mass spectrometric characterization is difficult due to the predominant occurrence of non-proteinogenic monomers and the complex fragmentation patterns observed. Even though several software tools for cyclic peptide tandem mass spectra annotation have been published, these tools are still unable to annotate a major...