Let q > 1 denote an integer relatively prime to 2, 3, 7 and for which G = PSL(2, q) is a Hurwitz group for a smooth projective curve X defined over C. We compute the G-module structure of the RiemannRoch space L(D), where D is an invariant divisor on X of positive degree. This depends on a computation of the ramification module, which we give explicitly. In particular, we obtain the decompositi...

The concepts of free modules, projective modules, injective modules, and the like form an important area in module theory. The notion of free fuzzy modules was introduced by Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameri introduced the concept of projective and injective L-modules. In this paper, we give an alternate definition for injective L-modules and prove t...

We define the Conway skein module C(M) of ordered based links in a 3-manifold M . This module gives rise to C(M)-valued invariants of usual links in M . Let F = Σ× [0, 1] where Σ is the real projective plane or a surface with boundary. In this case C(F ) is in a natural way an algebra. We determine a basis of the Z[z]-module C#(F ) = C(F )/Tor(C(F )). When Σ is the Möbius strip or the projectiv...

Let k be a field, G an abelian group with a bicharacter, A a colour algebra; i.e., an associative graded k-algebra with identity, C a graded A-coring that is projective as a right A-module, C∗ the graded dual ring of C and Λ a left graded C-comodule that is finitely generated as a graded right C∗-module. We give necessary and sufficient conditions for projectivity and flatness of a graded modul...

By a careful investigation of the model theory of modules over a special class of uniserial domains we give some (counter) examples to a decomposition of a serial module. For instance there is a uniserial module M over a uniserial domain that is not quasi-small. Also there is a projective non–free countably generated module over the endomorphism ring of M . MSC: 16D70; 16D99; 03C60

Let k be a commutative ring, A a k-algebra, C an A-coring that is projective as a left A-module, ∗C the dual ring of C and Λ a right C-comodule that is finitely generated as a left ∗C-module. We give necessary and sufficient conditions for projectivity and flatness of a module over the endomorphism ring EndC(Λ). If C contains a grouplike element, we can replace Λ with A.

We introduce a notion of permutation presentations of modules over finite groups, and completely determine finite groups over which every module has a permutation presentation. To get this result, we prove that every coflasque module over a cyclic p-group is permutation projective.

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.