In this paper, the concepts of minimal and maximal left hyperideals in ordered semihypergroups are introduced, and several related properties are investigated. Furthermore, we introduce the concepts of weakly prime, quasi-prime, quasi-semiprime and weakly quasiprime left hyperideals of an ordered semihypergroup, and establish the relationship among the four classes of left hyperideals. Moreover...

In this paper, we describe $ss$-supplement submodules in terms of a special class endomorphisms. Let $R$ be ring with semisimple radical and $P$ projective $R-$module. We show that there is bijection between ss-supplement $End_{R}(P)$. Moreover, define radical-s-projective modules as generalization modules. prove every submodule $R-$module over the radical. $SSI$-ring $R$, projective. provide r...

We introduce and investigate the notion of weak projection invariant semisimple modules. deal with structural properties this new class In trend we have indecomposable decompositions special former modules via some module theoretical properties. As a consequence, obtain when finite exchange property implies full for latter

Let g be a (finite-dimensional) semisimple Lie algebra over the complex numbers C and let σ be an involution (i.e., an automorphism of order 2) of g. Let k (resp. p) be the +1 (resp. −1) eigenspace of σ. Then, k is a Lie subalgebra of g and p is a k-module under the adjoint action. In this paper we only consider those involutions σ such that p is an irreducible k-module. We fix a g-invariant no...

1. Introduction. Let © be a Lie algebra over a field A. A decomposition of © is a triple (ni, b, n2) of subalgebras of © such that ® = niffif)©n2 a vector space direct sum and such that [b, n,-]Cn< for 4 = 1, 2. In [5] we showed how one could "induce" ©-modules from b-modules in a natural manner. In this paper we prove a useable necessary and sufficient condition that a ©-module must satisfy in...

This paper studies the algebraic aspect of a general abelian coset theory with [DL2] as our main motivation. It is proved that the vacuum space ΩV (or the space of highest weight vectors) of a Heisenberg algebra in a general vertex operator algebra V has a natural generalized vertex algebra structure in the sense of [DL2] and that the vacuum space ΩW of a V -module W is a natural ΩV -module. Th...

The G-module structure of the cohomology groups of line bundles over the flag variety G/B for a semisimple algebraic group G is studied. It is proved that, generically, their socle filtrations satisfy the same sum formula as Andersen’s filtrations if Lusztig’s conjecture is true. Another purpose of this paper is to calculate the socle series of the H0’s for the p-regular weights close to a cham...

We construct the H-von Neumann regular radical for H-module algebras and show that it is an H-radical property. We obtain that the Jacobson radical of twisted graded algebra is a graded ideal. For twisted H-module algebra R, we also show that rj(R#σH) = rHj(R)#σH and the Jacobson radical of R is stable, when k is an algebraically closed field or there exists an algebraic closure F of k such tha...