Let LD8(1, 0) and LE8(1, 0) be the simple vertex operator algebras associated to untwisted affine Lie algebra ĝD8 and ĝE8 with level 1 respectively. In the 1980s by I. Frenkel, Lepowsky and Meurman as one of the many important preliminary steps toward their construction of the moonshine module vertex operator algebra, they use roots lattice showing that LD8(1, 0) can embed into LE8(1, 0) as a v...

Algebra Situs is a branch of mathematics which has its roots in Jones’ construction of his polynomial invariant of links and Drinfeld’s work on quantum groups. It encompasses the theory of quantum invariants of knots and 3-manifolds, algebraic topology based on knots, operads, planar algebras, q-deformations, quantum groups, and overlaps with algebraic geometry, non-commutative geometry and sta...

Let R be a ring, M a right R-module and (S,≤) a strictly ordered monoid. In this paper we will show that if (S,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a uniserial right [[RS,≤]] ]]-module if and only if M is a simple right R-module and S is a chain monoid.

This is a collection of papers in computational D-module theory. The scope is limited to computation of invariants of D-modules including functors of ho-mology algebra in D-modules. If there are papers which are not cited, please let me know them. [6] Castro, F. : Théorème de division pour les opérateurs diffèrentiels et calcul des multiplicités. Thèse de 3` eme cycle, Université de Paris 7, 19...

We provide a new algebraic description of the structure on the set of all unstable cohomology operations for a suitable generalised cohomology theory, E(−). Our description is as a graded and completed version of a Tall-Wraith monoid. The E-cohomology of a space X is a module for this Tall-Wraith monoid. We also show that the corresponding Hopf ring of unstable co-operations is a module for the...

In this paper we define $varphi$-Connes module amenability of a dual Banach algebra $mathcal{A}$ where $varphi$ is a bounded $w_{k^*}$-module homomorphism from $mathcal{A}$ to $mathcal{A}$. We are mainly concerned with the study of $varphi$-module normal virtual diagonals. We show that if $S$ is a weakly cancellative inverse semigroup with subsemigroup $E$ of idemp...

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. ‎$r$ ...

Abstract: Let be a commutative ring and be a unitary module. We define a semiprime submodule of a module and consider various properties of it. Also we define semi-radical of a submodule of a module and give a number of its properties. We define modules which satisfy the semi-radical formula and present the existence of such a module.  

We find the model completion of the theory modules over A, where A is a finitely generated commutative algebra over a field K. This is done in a context where the field K and the module are represented by sorts in the theory, so that constructible sets associated with a module can be interpreted in this language. The language is expanded by additional sorts for the Grassmanians of all powers of...

Lately two modules which aim to improve the modeling of human reasoning have been introduced into the ACT-R cognitive architecture – the Human Reasoning Module (HRM) and the Pre-Attentive and Attentive Vision Module (PAAV). This is a first attempt to create a domain-specific infrastructure as an extension of a cognitive architecture. The HRM defines the basic functionality of two different theo...