We make a first step towards a classification of simple generalized HarishChandra modules which are not Harish-Chandra modules or weight modules of finite type. For an arbitrary algebraic reductive pair of complex Lie algebras (g, k), we construct, via cohomological induction, the fundamental series F ·(p, E) of generalized Harish-Chandra modules. We then use F ·(p, E) to characterize any simpl...

The notion of intuitinitic (T, S)-fuzzy submodule in Module is introduced, and related properties are investigated. Mathematics Subject Classification: 08A72, 13C99

in this paper, the notion of fully idempotent modules is defined and it is shown that this notion inherits most of the essential properties of the usual notion of von neumann's regular rings. furthermore, we introduce the dual notion of fully idempotent modules (that is, fully coidempotent modules) and investigate some properties of this class of modules.

let $r$ be a commutative ring with identity and let $m$ be an $r$-module. a proper submodule $p$ of $m$ is called strongly prime submodule if $(p + rx : m)ysubseteq p$ for $x, yin m$, implies that $xin p$ or $yin p$. in this paper, we study more properties of strongly prime submodules. it is shown that a finitely generated $r$-module $m$ is artinian if and only if $m$ is noetherian and every st...

In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems LLL (Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this arti...

In earlier papers we studied direct limits (G,K) = lim −→ (Gn,Kn) of two types of Gelfand pairs. The first type was that in which the Gn/Kn are compact riemannian symmetric spaces. The second type was that in which Gn = Nn ⋊ Kn with Nn nilpotent, in other words pairs (Gn,Kn) for which Gn/Kn is a commutative nilmanifold. In each we worked out a method inspired by the Frobenius–Schur Orthogonalit...