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.

Let G be a group with identity e. R G-graded commutative ring and M graded R-module. We introduce the concept of Ie-prime submodule as generalization prime for I =?g?G Ig fixed ideal R. give number results concerning this class submodules their homogeneous components. A proper N is said to if whenever rg ? h(R) mh h(M) rgmh IeN, then either (N :R M) or N.

A tag module is a generalization, in any abelian category, of a torsion abelian group. The theory of such modules is developed, it is shown that countably generated tag modules are simply presented, and that Ulm's theorem holds for simply presented tag modules. Zippin's theorem is stated and proved for countably generated tag modules. 1. TAG-modules In the theory of torsion abelian groups, a di...

In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.

In this paper, for any prime $p$, we propose the notion of a $p$-transitive association scheme. This aims to generalize fact that regular module group algebra finite has unique trivial submodule case modules modular adjacency algebras. We completely determine quasi-thin schemes and with thin residue by their structure theory properties.

let $r$ be a commutative ring with identity and $m$ be a unitary$r$-module. the primary-like spectrum $spec_l(m)$ is thecollection of all primary-like submodules $q$ such that $m/q$ is aprimeful $r$-module. here, $m$ is defined to be rsp if $rad(q)$ isa prime submodule for all $qin spec_l(m)$. this class containsthe family of multiplication modules properly. the purpose of thispaper is to intro...

Let R be a commutative ring with nonzero identity and M an R-module. In this paper, first we give some relations between S-prime S-maximal submodules that are generalizations of prime maximal submodules, respectively. Then construct topology on the set all , which is generalization spectrum M. We investigate when SpecS(M) T0 T1-space. also study continuous maps irreducibility SpecS(M). Moreover...

The flavivirus bovine viral diarrhoea (BVD) virus exists in two biotypes, cytopathic (cp) and non-cytopathic (ncp), defined by their effect on cultured cells. Cp BVD virus-infected cells undergo apoptosis and may promote apoptosis in uninfected cells by an indirect mechanism. Macrophages (Mφ) infected with cp, but not ncp, BVD virus release a factor(s) in the supernatant capable of priming ...

If N is a submodule of the R-module M , and a ∈ R, let λa : M/N → M/N be multiplication by a. We say that N is a primary submodule of M if N is proper and for every a, λa is either injective or nilpotent. Injectivity means that for all x ∈ M , we have ax ∈ N ⇒ x ∈ N . Nilpotence means that for some positive integer n, aM ⊆ N , that is, a belongs to the annihilator of M/N , denoted by ann(M/N). ...