On reflexivity of representations of local Commutative Algebras
On regular presheaves and regular semi-categories
On Regular Rings and Self-Injective Rings.
On Regular Rings and Self-injective Rings, iv
On Regular Rings and V-Rings.
On relative homotopy groups of modules.
On restrictions of indecomposables of tame algebras
We continue the study of ditalgebras, an acronym for "differential tensor algebras", and of their categories of modules. We examine extension/restriction interactions between module categories over a ditalgebra and a proper subditalgebra. As an application, we prove a result on representations of finite-dimensional tame algebras Λ over an algebraically closed field, which gives information on the extension/restriction interaction between module categories of some special algebras Λ₀, called convex...
On rings all of whose modules are retractable
Let be a ring. A right -module is said to be retractable if whenever is a non-zero submodule of . The goal of this article is to investigate a ring for which every right R-module is retractable. Such a ring will be called right mod-retractable. We proved that The ring is right mod-retractable if and only if each is a right mod-retractable ring for each , where is an arbitrary finite set. If is a mod-retractable ring then is a mod-retractable ring.
On rings close to regular and -injectivity
The following results are proved for a ring : (1) If is a fully right idempotent ring having a classical left quotient ring which is right quasi-duo, then is a strongly regular ring; (2) has a classical left quotient ring which is a finite direct sum of division rings iff is a left -ring having a reduced maximal right ideal and satisfying the maximum condition on left annihilators; (3) Let have the following properties: (a) each maximal left ideal of is either a two-sided ideal...
On rings whose flat modules form a Grothendieck category
On rings with a unique proper essential right ideal
Right ue-rings (rings with the property of the title, i.e., with the maximality of the right socle) are investigated. It is shown that a semiprime ring R is a right ue-ring if and only if R is a regular V-ring with the socle being a maximal right ideal, and if and only if the intrinsic topology of R is non-discrete Hausdorff and dense proper right ideals are semisimple. It is proved that if R is a right self-injective right ue-ring (local right ue-ring), then R is never semiprime and is Artin semisimple...
On Rings with Polynomial Identity xn-x=0
On rings with zero total.
On selfinjective algebras of Euclidean type
On selfinjective algebras of tilted type
We provide a characterization of all finite-dimensional selfinjective algebras over a field K which are socle equivalent to a prominent class of selfinjective algebras of tilted type.
On selfinjective algebras without short cycles in the component quiver
We give a complete description of all finite-dimensional selfinjective algebras over an algebraically closed field whose component quiver has no short cycles.
On selfinjective artin algebras having nonperiodic generalized standard Auslander-Reiten components
We describe the structure of all selfinjective artin algebras having at least three nonperiodic generalized standard Auslander-Reiten components. In particular, all selfinjective artin algebras having a generalized standard Auslander-Reiten component of Euclidean type are described.
On simple distributively generated near-rings
On small injective, simple-injective and quasi-Frobenius rings.
On some classes of modules
The aim of this paper is to investigate quasi-corational, comonoform, copolyform and -(co)atomic modules. It is proved that for an ordinal a right -module is -atomic if and only if it is -coatomic. And it is also shown that an -atomic module is quasi-projective if and only if is quasi-corationally complete. Some other results are developed.