The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and only if it is multiplication and idempotent. Various properties and characterizations of pure submodules of multiplication modules are consid...

The purpose of this paper is to introduce a new concept in module M over ring R, called e∗-essential submodule, which generalization an essential submodule. We will some examples and properties about such that, what the inverse image intersection submodules direct sum submodules. show relationship between submodule Noetherian R-module. Also we define e∗-closed with

Irreducible covariant tensor modules for the Lie supergroups GL(m/n) and the Lie superalgebras gl(m/n) and sl(m/n) are obtained through the use of Young tableaux techniques. The starting point is the graded permutation action, first introduced by Dondi and Jarvis, on V. The isomorphism between this group of actions and the symmetric group Sl enables the graded generalization of the Young symmet...

In this article, we review some aspects of logarithmic conformal field theories which can be inferred from the characters of irreducible submodules of indecomposable modules. We will mainly consider the W(2, 2p− 1, 2p− 1, 2p− 1) series of triplet algebras and a bit logarithmic extensions of the minimal Virasoro models. Since in all known examples of logarithmic conformal field theories the vacu...

We prove Wigner-Eckart theorem for the irreducible tensor operators for arbitrary Hopf algebras, provided that tensor product of their irreducible representation is completely reducible. The proof is based on the properties of the irreducible representations of Hopf algebras, in particular on Schur lemma. Two classes of tensor operators for the Hopf algebra Ut(su(2)) are considered. The reduced...

The complement operation on modules has not been argued so far as we know. We observe that it plays an important role in software maintenance, as well as join and meet operations. A de nition of a module and operations on them is given in category theoretic terms; we adopt well-known characterization of complement as a left adjoint to join. The de nition is rst given locally and then extended t...

It has been observed by different authors that QTAG-modules behave very much like torsion abelian groups. In this paper, in section 3, we characterize quasi-essential submodules (Theorem 3.9) and further find a characterization for an h-pure submodule to be a direct summand (Theorem 3.11). In section 4, we obtained a necessary and sufficient condition for a submodule to be contained in a minima...

A module M is called ?-?ss-supplemented if every submodule X of has a ?ss-supplement Y in which direct summand such that + = and ? Soc? (Y) where Soc?(Y) the sum simple ?-small submodules Y? for some M. Moreover, completely ?-?ss-supplemented. Thus, we present two new types algebraic structures are stronger than ?-D11 ?-D+11-modules, respectively. In this paper investigate basic properties, dec...

There proved that every prime invariant with respect to quantum adjoint action ideal I is completely prime and Fract(R/I) is isomorphic to the skew field of fractions of an algebra of twisted polynomials. We study correspondence between symplectic leaves and irreducible representations. The Conjecture of De Concini-KacProcesi on dimension of irreducible representations is proved for sufficientl...

Munn [9] has shown that for a semigroup S satisfying the minimal condition on principal ideals, there is a natural one-to-one correspondence between irreducible representations of S and irreducible representations vanishing at zero of its 0-simple (or simple) principal factors; for the case of S finite, see Ponizovskii [11]. On the other hand, Clifford, [3] and [4], has obtained all representat...