Let A be a finite dimensional hereditary algebra over an algebraically closed field k, A(m) be the m-replicated algebra of A and Cm(A) be the m-cluster category of A. We investigate properties of complements to a faithful almost complete tilting A(m)-module and prove that the m-cluster mutation in Cm(A) can be realized in mod A (m), which generalizes corresponding results on duplicated algebras...

In this article we prove conditions under which a certain parabolic group cohomology space over a finite field F is a faithful module for the Hecke algebra of Katz modular forms over an algebraic closure of F. These results can e.g. be used to compute Katz modular forms of weight one with methods of linear algebra over F. MSC Classification: 11F25 (primary), 11F33, 11F67, 11Y40 (secondary).

In this paper we survey some work on representations of Bn given by the induced action on a homology module of some space. One of these, called the Lawrence-Krammer representation, recently came to prominence when it was shown to be faithful for all n. We will outline the methods used, applying them to a closely related representation for which the proof is slightly easier. The main tool is the...

To a B-coring and a (B, A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projec...

We introduce the notion of Burch submodules and weakly m-full modules over a local ring (R,m) study their properties. One our main results shows that satisfy 2-Tor rigid test also show (R,m), submodule M finitely generated R-module X, such either M=mX or M(⊆mX) is in 1-Tor rigid, module provided X faithful (and X∕M has finite length when m-full). As an application, we give some new class rings ...

In this paper we study the class of laterally complete commutative unital regular algebras A over arbitrary fields. We introduce a notion passport Γ(X) for faithful Amodules X, which consist uniquely defined partition unity in Boolean algebra all idempotents and set pairwise different cardinal numbers. prove that A-modules X Y are isomorphic if only = Γ(Y). Further Banach case C∞(Q) or C∞(Q)+i ...

This article focuses on the role loyalty played in relationship between rulers and their subjects earliest Central European chronicles, written at beginning of twelfth century: Gesta principum Polonorum by Gallus Anonymous, Chronica Boemorum Cosmas Prague, twelfth-century historiographical tradition Hungarian Royal court, which survived as a part fourteenth-century century compilation called Th...

To a B-coring and a (B, A)-bimodule that is finitely generated and projective as a right A-module an A-coring is associated. This new coring is termed a base ring extension of a coring by a module. We study how the properties of a bimodule such as separability and the Frobenius properties are reflected in the induced base ring extension coring. Any bimodule that is finitely generated and projec...

Let R be a commutative ring with non-zero identity, S multiplicatively closed subset of and M unital R-module. In this paper, we define submodule N (N :R M) ? = to weakly S-primary if there exists s such that whenever m 0 , am N, then either sa ??(N or sm N. We present various properties characterizations concept (especially in faithful multiplication modules). Moreover, the behavior structure ...

In the setting of geometric Langlands conjecture, we argue that phenomenon divergence at infinity on Bun_G (that is, difference between $!$-extensions and $*$-extensions) is controlled, Langlands-dually, by locus semisimple $\check{G}$-local systems. To see this, first rephrase question in terms Deligne-Lusztig duality then study functor DL_G^\spec acting spectral DG category IndCoh_N(LS_G). We...