About relationship between generalized structurable algebras and Lie related triples.
About the naturality of Beattie's decomposition theorem with respect to a change of Hopf algebras
Absolute stable rank and Witt cancellation for noncommutative rings.
Actions of Hopf algebras on fully bounded Noetherian rings.
Actions of Hopf algebras on pro-semisimple noetherian algebras and their invariants
Let H be a Hopf algebra over a field k such that every finite-dimensional (left) H-module is semisimple. We give a counterpart of the first fundamental theorem of the classical invariant theory for locally finite, finitely generated (commutative) H-module algebras, and for local, complete H-module algebras. Also, we prove that if H acts on the k-algebra A = k[[X₁,...,Xₙ]] in such a way that the unique maximal ideal in A is invariant, then the algebra of invariants is a noetherian Cohen-Macaulay...
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...
Actions of the additive group on certain noncommutative deformations of the plane
We connect the theorems of Rentschler [rR68] and Dixmier [jD68] on locally nilpotent derivations and automorphisms of the polynomial ring and of the Weyl algebra , both over a field of characteristic zero, by establishing the same type of results for the family of algebras where is an arbitrary polynomial in . In the second part of the paper we consider a field of prime characteristic and study comodule algebra structures on . We also compute the Makar-Limanov invariant of absolute constants...
Acyclicity versus total acyclicity for complexes over noetherian rings.
of a uniserial module
A module is called uniserial if it has totally ordered submodules in inclusion. We describe direct summands of for a uniserial module . It appears that any such a summand is isomorphic to a direct sum of copies of at most two uniserial modules.
Addendum to "Generalized radical rings, unknotted biquandles, and quantum groups" (Colloq. Math. 109 (2007), 85-100)
Addendum to “Hochschild cohomology of skew group rings and invariants”
Addendum to “Ring elements as sums of units”
We give a comment to Theorem 1.1 published in our paper “Ring elements as sums of units” [Cent. Eur. J. Math., 2009, 7(3), 395–399].
Addendum to "Rings whose modules have maximal submodules".
Addendum to the author's article "Rings whose modules have maximal submodules", which appeared in Publicacions Matemàtiques 39, 1 (1995), 201-214.
Addendum to Zip rings.
We list some typos and minor correction that in no way affect the main results of Rings with zero intersection property on annihilators: Zip rings (Publicacions Matemàtiques 33, 2 (1989), pp. 329-338), e.g., nothing stated in the abstract is affected.
Addendum zu: Quasi-Frobenius-Algebren und lokal vollständige Durchschnitte:
Additive deformations of braided Hopf algebras
Additive deformations of bialgebras in the sense of J. Wirth [PhD thesis, Université Paris VI, 2002], i.e. deformations of the multiplication map fulfilling a certain compatibility condition with respect to the coalgebra structure, can be generalized to braided bialgebras. The theorems for additive deformations of Hopf algebras can also be carried over to that case. We consider *-structures and prove a general Schoenberg correspondence in this context. Finally we give some examples.
Additive Duality at Cosmall Injectives
Additive functions for quivers with relations
Additive functions for quivers with relations extend the classical concept of additive functions for graphs. It is shown that the concept, recently introduced by T. Hübner in a special context, can be defined for different homological levels. The existence of such functions for level 2 resp. ∞ relates to a nonzero radical of the Tits resp. Euler form. We derive the existence of nonnegative additive functions from a family of stable tubes which stay tubes in the derived category, we investigate when...
Additive functions on trees
The motivation for considering positive additive functions on trees was a characterization of extended Dynkin graphs (see I. Reiten [R]) and applications of additive functions in representation theory (see H. Lenzing and I. Reiten [LR] and T. Hübner [H]). We consider graphs equipped with integer-valued functions, i.e. valued graphs (see also [DR]). Methods are given for constructing additive functions on valued trees (in particular on Euclidean graphs) and for characterizing...
Additive radicals