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Squared cycles in monomial relations algebras

Brian Jue (2006)

Open Mathematics

Let 𝕂 be an algebraically closed field. Consider a finite dimensional monomial relations algebra Λ = 𝕂 Γ 𝕂 Γ I I of finite global dimension, where Γ is a quiver and I an admissible ideal generated by a set of paths from the path algebra 𝕂 Γ . There are many modules over Λ which may be represented graphically by a tree with respect to a top element, of which the indecomposable projectives are the most natural example. These trees possess branches which correspond to right subpaths of cycles in the quiver. A pattern...

Stability of commuting maps and Lie maps

J. Alaminos, J. Extremera, Š. Špenko, A. R. Villena (2012)

Studia Mathematica

Let A be an ultraprime Banach algebra. We prove that each approximately commuting continuous linear (or quadratic) map on A is near an actual commuting continuous linear (resp. quadratic) map on A. Furthermore, we use this analysis to study how close are approximate Lie isomorphisms and approximate Lie derivations to actual Lie isomorphisms and Lie derivations, respectively.

Standardly stratified split and lower triangular algebras

Eduardo do N. Marcos, Hector A. Merklen, Corina Sáenz (2002)

Colloquium Mathematicae

In the first part, we study algebras A such that A = R ⨿ I, where R is a subalgebra and I a two-sided nilpotent ideal. Under certain conditions on I, we show that A is standardly stratified if and only if R is standardly stratified. Next, for A = U 0 M V , we show that A is standardly stratified if and only if the algebra R = U × V is standardly stratified and V M is a good V-module.

Stratified modules over an extension algebra

Erzsébet Lukács, András Magyar (2018)

Czechoslovak Mathematical Journal

Let A be a standard Koszul standardly stratified algebra and X an A -module. The paper investigates conditions which imply that the module Ext A * ( X ) over the Yoneda extension algebra A * is filtered by standard modules. In particular, we prove that the Yoneda extension algebra of A is also standardly stratified. This is a generalization of similar results on quasi-hereditary and on graded standardly stratified algebras.

Strict Mittag-Leffler conditions and locally split morphisms

Yanjiong Yang, Xiaoguang Yan (2018)

Czechoslovak Mathematical Journal

In this paper, we prove that any pure submodule of a strict Mittag-Leffler module is a locally split submodule. As applications, we discuss some relations between locally split monomorphisms and locally split epimorphisms and give a partial answer to the open problem whether Gorenstein projective modules are Ding projective.

Strong no-loop conjecture for algebras with two simples and radical cube zero

Bernt T. Jensen (2005)

Colloquium Mathematicae

Let Λ be an artinian ring and let 𝔯 denote its Jacobson radical. We show that a simple module of finite projective dimension has no self-extensions when Λ is graded by its radical, with at most two simple modules and 𝔯⁴ = 0, in particular, when Λ is a finite-dimensional algebra over an algebraically closed field with at most two simple modules and 𝔯³ = 0.

Currently displaying 161 – 180 of 274