Idempotent Boolean matrices.
Independence in Completions and Endomorphism Algebras.
Integral schur algebras for GL2.
Involution Matrix Algebras – Identities and Growth
2000 Mathematics Subject Classification: 16R50, 16R10.The paper is a survey on involutions (anti-automorphisms of order two) of different kinds. Starting with the first systematic investigations on involutions of central simple algebras due to Albert the author emphasizes on their basic properties, the conditions on their existence and their correspondence with structural characteristics of the algebras. Focusing on matrix algebras a complete description of involutions of the first kind on Mn(F)...
Isomorphism of generalized triangular matrix-rings and recovery of tiles.
Iterated tilted and tilted stably hereditary algebras
We prove that a stably hereditary bound quiver algebra A = KQ/I is iterated tilted if and only if (Q,I) satisfies the clock condition, and that in this case it is of type~Q. Furthermore, A is tilted if and only if (Q,I) does not contain any double-zero.
Jordan automorphisms, Jordan derivations of generalized triangular matrix algebra.
Jordan left derivations in full and upper triangular matrix rings.
Koszul and quasi-Koszul algebras obtained by tilting
Given a finite-dimensional algebra, we present sufficient conditions on the projective presentation of the algebra modulo its radical for a tilted algebra to be a Koszul algebra and for the endomorphism ring of a tilting module to be a quasi-Koszul algebra. One condition we impose is that the algebra has global dimension no greater than 2. One of the main techniques is studying maps between the direct summands of the tilting module. Some applications are given. We also show that a Brenner-Butler...
Linearly compact rings and strongly quasi-injective modules
Localisations premières
Locally free modules
Logics that are generated by idempotents.
-density, -adic completion and -subgeneration
Matrices carrées sur l'algèbre de Weyl
Matrices over upper triangular bimodules and Δ-filtered modules over quasi-hereditary algebras
Let Λ be a directed finite-dimensional algebra over a field k, and let B be an upper triangular bimodule over Λ. Then we show that the category of B-matrices mat B admits a projective generator P whose endomorphism algebra End P is quasi-hereditary. If A denotes the opposite algebra of End P, then the functor Hom(P,-) induces an equivalence between mat B and the category ℱ(Δ) of Δ-filtered A-modules. Moreover, any quasi-hereditary algebra whose category of Δ-filtered modules is equivalent to mat...
Matrix rings with summand intersection property
A ring has right SIP (SSP) if the intersection (sum) of two direct summands of is also a direct summand. We show that the right SIP (SSP) is the Morita invariant property. We also prove that the trivial extension of by has SIP if and only if has SIP and for every idempotent in . Moreover, we give necessary and sufficient conditions for the generalized upper triangular matrix rings to have SIP.
Modules Over Arbitrary Domains.
Modules over arbitrary domains II
Modules Over Matrix Near-Rings and the ...-Radical.