let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

In our recent work we gave a treatment of certain aspects of multiplication modules, projective modules, flat modules and cancellation-like modules via idealization. The purpose of this work is to continue our study and develop the tool of idealization, particularly in the context of closed, divisible injective, and simple modules. We determine when a ring R (M), the idealization of M , is a qu...

In this paper we use A∞-modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A∞-modules. These varieties carry an action of an algebraic group such that orbits correspond to quasi-isomorphism classes of complexes in the derived category. We describe orbit closures in these varieties, generalising a result of ...

In this paper we use A∞-modules to study the derived category of a finite dimensional algebra over an algebraically closed field. We study varieties parameterising A∞-modules. These varieties carry an action of an algebraic group such that orbits correspond to quasiisomorphism classes of complexes in the derived category. We describe orbit closures in these varieties, generalising a result of Z...

A module M is called product closed if every hereditary pretorsion class in σ[M ] is closed under products in σ[M ]. Every module which is locally of finite length is product closed and every product closed module is semilocal. LetM ∈ R-Mod be product closed and projective in σ[M ]. It is shown that (1) M is semiartinian; (2) if M is finitely generated then M satisfies the DCC on fully invarian...

We consider separably closed fields of characteristic p > 0 and fixed Imperfection degree as modules over a skew polynomial ring. We axlotnatlze the correspondltlg theory and ue show that i t is complete and that ~t adnilts quantifier e l ~ n i ~ n a t ~ o n In the usual nlodule language augmented with additwe functions whlch are the analog of the p-component functions. $

In Dellunde et al. (J. Symbolic Logic 67(3) (2002) 997–1015), we determined the complete theory Te of modules of separably closed %elds of characteristic p and imperfection degree e, e∈! ∪ {∞}. Here, for 0 = e∈!, we describe the closed set of the Ziegler spectrum corresponding to Te. Further, we establish a correspondence between certain submodules and n-types and we investigate several notions...