Exact indecomposable module categories over the tensor category of representations of Hopf algebras that are liftings of quantum linear spaces are classified.

We study the H n ( 0 ) -module S ? ? due to Tewari and van Willigenburg, which was constructed using new combinatorial objects called standard permuted composition tableaux decomposed into cyclic submodules. First, we show that every direct summand appearing in their decomposition is indecomposable characterize when indecomposable. Second, find characteristic relations among 's expand image of ...

It is proved in this paper that an irreducible module over the non-graded Virasoro-like algebra L, which satisfies a natural condition, is a GHW module or uniformly bounded. Furthermore, we give the complete classification of indecomposable L-modules V = ⊕ m,n∈Z Cvm,n which satisfy Lr,svm,n ⊆ Cvr+m,s+n+1 + Cvr+m,s+n.

Let (A, m, k) be a complete intersection of codimension c, and k̃ the algebraic closure of k. We show that every homogeneous algebraic subset of k̃c is the cohomological support variety of an A-module, and that the projective variety of a complete indecomposable maximal Cohen-Macaulay A-module is connected.

On the space of homomorphisms from a Verma module to an indecomposable tilting module of the BGG-category O we define a natural filtration following Andersen [And97] and establish a formula expressing the dimensions of the filtration steps in terms of coefficients of Kazhdan-Lusztig polynomials.

It is proved that a commutative ring is clean if and only if it is Gelfand with a totally disconnected maximal spectrum. It is shown that each indecomposable module over a commutative ring R satisfies a finite condition if and only if R P is an artinian valuation ring for each maximal prime ideal P. Commutative rings for which each indecomposable module has a local endomorphism ring are studied...

It is proved that any cluster-tilted algebra defined in the cluster category C(H) has the same representation type as the initial hereditary algebra H . For any valued quiver (Γ,Ω), an injection from the subset PI(Ω) of the cluster category C(Ω) consisting of indecomposable preprojective objects, preinjective objects and the first shifts of indecomposable projective modules to the set of cluste...

The only groups for which all indecomposable modules are ‘knowable’ are those with cyclic, dihedral, semidihedral, and quaternion Sylow p-subgroups. The structure of the Green ring for groups with cyclic and V4 Sylow p-subgroups are known, but no others have been determined. Of the remaining groups, the dihedral 2-groups have the simplest module category but yet the tensor products of any two i...

We state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. In particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. Also we show that if M is an strong comultiplicati...