BRST-resolution is studied for the principally graded Wakimoto module of ŝl2 recently found in [9]. The submodule structure is completely determined and irreducible representations can be obtained as the zero-th cohomology group. e-mail:[email protected]

The cross-characteristic permutation modules for the actions of the finite classical groups on singular 1-spaces of their natural modules are studied. The composition factors and submodule lattices are determined.

Altered brain morphometry has been widely acknowledged in chronic pain, and recent studies have implicated altered network dynamics, as opposed to properties of individual brain regions, in supporting persistent pain. Structural covariance analysis determines the inter-regional association in morphological metrics, such as gray matter volume, and such structural associations may be altered in c...

All rings are commutative with identity and all modules are unital. Let R be a ring, M an R-module and R (M), the idealization of M . Homogeneous ideals of R (M) have the form I (+)N where I is an ideal of R, N a submodule of M and IM ⊆ N . The purpose of this paper is to investigate how properties of a homogeneous ideal I (+)N of R (M) are related to those of I and N . We show that if M is a m...

Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $\theta$ automorphism of induced from $-1$-isometry and $V_{L}^{+}$ fixed point subalgebra under action $\theta$. In this series papers, we classify irreducible weak $V_{L}^{+}$-modules show that any $V_{L}^{+}$-module is isomorphic submodule some $V_{L}$-module or $\theta$-twisted $V_{L}$-module. paper (Part 1),...

We provide an upper bound of the dimension of the maximal projective submodule of the Lie module of the symmetric group of n letters in prime characteristic p, where n = pk with p k.

Let R be a commutative ring with identity and let M unitary R-module. In this paper, we introduce the notion of weakly S-2-absorbing submodule. Suppose that S is multiplicatively closed subset R. A submodule P (P:R M)∩S=∅ said to if there exists an element s ∈ such whenever a,b∈R m∈M 0≠abm∈P, then sab∈(P: M) or sam∈P sbm∈P. We give characterizations, properties examples submodules.