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. $

Let ${\Bbbk }$ be an algebraically closed field, let Λ a finite dimensional -algebra, and $\widehat {\Lambda the repetitive algebra of Λ. For stable category finitely generated left -modules -mod, we prove that every Auslander-Reiten triangle in -mod is induced from sequence -modules. We use this fact to show irreducible morphisms fall into three canonical forms: (i) all component are split mon...

let $r$ be an arbitrary ring with identity and $m$ a right $r$-module with $s=$ end$_r(m)$. the module $m$ is called {it rickart} if for any $fin s$, $r_m(f)=se$ for some $e^2=ein s$. we prove that some results of principally projective rings and baer modules can be extended to rickart modules for this general settings.

A cohomological support, Supp A (M), is defined for finitely generated modules M over a left noetherian ring R, with respect to a ring A of central cohomology operations on the derived category of R-modules. It is proved that if the A-module Ext R (M, M) is noetherian and Ext R (M, R) = 0 for i ≫ 0, then every closed subset of Supp A (M) is the support of some finitely generated R-module. This ...

We introduce a suitable adapted ordering for the twisted N = 2 superconformal algebra (i.e. with mixed boundary conditions for the fermionic fields). We show that the ordering kernels for complete Verma modules have two elements and the ordering kernels for G-closed Verma modules just one. Therefore, spaces of singular vectors may be two-dimensional for complete Verma modules whilst for G-close...

In this paper we study wide subcategories. A full subcategory of R-modules is said to be wide if it is abelian and closed under extensions. Hovey [Hov01] gave a classification of wide subcategories of finitely presented modules over regular coherent rings in terms of certain specialisation closed subsets of Spec(R). We use this classification theorem to study K-theory and “Krull-Schmidt” decomp...

In this notes unbounded regular operators on Hilbert C∗-modules over arbitrary C∗-algebras are discussed. A densely defined closed operator t possesses a densely defined adjoint operator if the graph of t is an orthogonal summand. Moreover, for a densely defined closed operator t the graph of t is orthogonally complemented if and only if t is regular. For a given C*-algebra A any densely define...