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...

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.

This article introduces the concept of S-2-absorbing primary submodule as a generalization 2-absorbing submodule. Let S be multiplicatively closed subset ring R and M an R-module. A proper N is said to if (N :R M) ? = there exists fixed element s such that whenever abm for some a,b m M, then either sam or sbm sab ?(N M). We give several examples, properties characterizations related concept. Mo...