A bicategorical approach to static modules.
A brief review of abelian categorifications.
A canonical directly infinite ring
Let be the set of nonnegative integers and the ring of integers. Let be the ring of matrices over generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of yields that the subrings generated by them coincide. This subring is the sum of the ideal consisting of...
A categorification of the square root of -1
We give a graphical calculus for a monoidal DG category ℐ whose Grothendieck group is isomorphic to the ring ℤ[√(-1)]. We construct a categorical action of ℐ which lifts the action of ℤ[√(-1)] on ℤ².
A characterization of discrete linearly compact rings by means of a duality
A Characterization Of Primal Noetherian Rings.
A characterization of the Artinian modules.
A Class of Balanced Non-Uniserial Rings.
A class of quasitilted rings that are not tilted
Based on the work of D. Happel, I. Reiten and S. Smalø on quasitilted artin algebras, the first two authors recently introduced the notion of quasitilted rings. Various authors have presented examples of quasitilted artin algebras that are not tilted. Here we present a class of right quasitilted rings that not right tilted, and we show that they satisfy a condition that would force a quasitilted artin algebra to be tilted.
A class of rings which are algebraic over the integers.
A classification of symmetric algebras of strictly canonical type
In continuation of our article in Colloq. Math. 116.1, we give a complete description of the symmetric algebras of strictly canonical type by quivers and relations, using Brauer quivers.
A decomposition theorem for comodules
A duality result for almost split sequences
Over an artinian hereditary ring R, we discuss how the existence of almost split sequences starting at the indecomposable non-injective preprojective right R-modules is related to the existence of almost split sequences ending at the indecomposable non-projective preinjective left R-modules. This answers a question raised by Simson in [27] in connection with pure semisimple rings.
A family of noetherian rings with their finite length modules under control
We investigate the category of finite length modules over the ring , where is a V-ring, i.e. a ring for which every simple module is injective, a subfield of its centre and an elementary -algebra. Each simple module gives rise to a quasiprogenerator . By a result of K. Fuller, induces a category equivalence from which we deduce that . As a consequence we can (1) construct for each elementary -algebra over a finite field a nonartinian noetherian ring such that , (2) find twisted...
A functional equation for quadratic forms.
A functional treatment of right invariant holoids.
A functor between categories of regular modules for wild hereditary algebras.
A functor-valued invariant of tangles.
A general concept of the pseudoprojective module
A general form of non-Frobenius self-injective algebras
Applying the classical work of Nakayama [Ann. of Math. 40 (1939)], we exhibit a general form of non-Frobenius self-injective finite-dimensional algebras over a field.