Splitting of Hermitian Forms over Group Rings.
Square subgroups of rank two abelian groups
Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.
Squared cycles in monomial relations algebras
Let be an algebraically closed field. Consider a finite dimensional monomial relations algebra of finite global dimension, where Γ is a quiver and I an admissible ideal generated by a set of paths from the path algebra . 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...
s-rings and modular representations.
Stability of commuting maps and Lie maps
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.
Stable and costable preradicals
Stable Clifford theory for divisorially graded rings.
Stable equivalences of Morita type for self-injective algebras and p-groups.
Stable rings generated by their units.
Stably flat completions of universal enveloping algebras [Book]
Stably free, projective right ideals
Standard character condition for table algebras.
Standardly stratified split and lower triangular algebras
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 , we show that A is standardly stratified if and only if the algebra R = U × V is standardly stratified and is a good V-module.
Starting and ending components of the Auslander-Reiten quivers of a class of special biserial algebras
The class of n-fundamental algebras is introduced. It is a subclass of string algebras. For n-fundamental algebras we study the problem of when the Auslander-Reiten quiver contains, at the beginning or at the end, a component which is not generalized standard.
Steady ideals and rings
Steinitz classes of central simple algebras
Stiff derivations of commutative rings
Stratified modules over an extension algebra
Let be a standard Koszul standardly stratified algebra and an -module. The paper investigates conditions which imply that the module over the Yoneda extension algebra is filtered by standard modules. In particular, we prove that the Yoneda extension algebra of 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
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 commutativity preserving maps on Lie ideals of semiprime rings.