A radical between Jacobson and Brown-McCoy radicals
A Reduction Theorem for the Primitivity of Tensor Products.
A remark about the Connes fusion tensor product.
A remark on decomposable modules.
A remark on -torsion-free modules
A Remark on Projective Dimension of Fiat Modules.
A Remark on Pure Ideals and Projective Modules.
A Remark on tilting theory and DG algebras.
A short proof of Krull's intersection theorem
A splitting theorem for ℱ-products
A structure theorem for right invariant right holoids.
A subclass of strongly clean rings
In this paper, we introduce a subclass of strongly clean rings. Let be a ring with identity, be the Jacobson radical of , and let denote the set of all elements of which are nilpotent in . An element is called very -clean provided that there exists an idempotent such that and or is an element of . A ring is said to be very -clean in case every element in is very -clean. We prove that every very -clean ring is strongly -rad clean and has stable range one. It is shown...
A surjectivity theorem for rigid highest weight modules.
A Survey of Rings Generated by Units
This article presents a brief survey of the work done on rings generated by their units.
A theorem on direct products of Slender modules
A theoreme on derivations in semiprime rings.
A weaker form of Baer’s splitting problem for torsion theories
Abelian group pairs having a trivial coGalois group
Torsion-free covers are considered for objects in the category Objects in the category are just maps in -Mod. For we find necessary and sufficient conditions for the coGalois group associated to a torsion-free cover, to be trivial for an object in Our results generalize those of E. Enochs and J. Rado for abelian groups.
Abelian groups which have trivial absolute coGalois group
In this article we characterize those abelian groups for which the coGalois group (associated to a torsion free cover) is equal to the identity.
Actions of parabolic subgroups in GL_n on unipotent normal subgroups and quasi-hereditary algebras
Let R be a parabolic subgroup in . It acts on its unipotent radical and on any unipotent normal subgroup U via conjugation. Let Λ be the path algebra of a directed Dynkin quiver of type with t vertices and B a subbimodule of the radical of Λ viewed as a Λ-bimodule. Each parabolic subgroup R is the group of automorphisms of an algebra Λ(d), which is Morita equivalent to Λ. The action of R on U can be described using matrices over the bimodule B. The advantage of this description is that each...