Shoikhet's conjecture and Duflo isomorphism on (co)invariants.
Simple Regular Rings and Rank Functions.
Simply connected right multipeak algebras and the separation property
Let R=k(Q,I) be a finite-dimensional algebra over a field k determined by a bound quiver (Q,I). We show that if R is a simply connected right multipeak algebra which is chord-free and -free in the sense defined below then R has the separation property and there exists a preprojective component of the Auslander-Reiten quiver of the category prin(R) of prinjective R-modules. As a consequence we get in 4.6 a criterion for finite representation type of prin(R) in terms of the prinjective Tits quadratic...
Singularity categories of skewed-gentle algebras
Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let and be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of . As a corollary, we find that if and only if if and only if .
SK... for finite group rings: II.
SK1 of finite abelian groups. I.
SK1 of finite group rings: V.
SK1 von Algebren über vollständig diskret bewerteten Körpern und Galoiskohomologie abelscher Körpererweiterungen.
SKi of fmite abelian groups, II.
Small models for chain algebras.
Smooth algebras and vanishing of Hochschild homology.
Sobre anillos de polinomios que son anillos de Bézout.
Solutions of minus partial ordering equations over von Neumann regular rings
In this paper, we mainly derive the general solutions of two systems of minus partial ordering equations over von Neumann regular rings. Meanwhile, some special cases are correspondingly presented. As applications, we give some necessary and sufficient conditions for the existence of solutions. It can be seen that some known results can be regarded as the special cases of this paper.
Some characterizations of regular modules.
Let M be a left module over a ring R. M is called a Zelmanowitz-regular module if for each x ∈ M there exists a homomorphism F: M → R such that f(x) = x. Let Q be a left R-module and h: Q → M a homomorphism. We call h locally split if for every x ∈ M there exists a homomorphism g: M → Q such that h(g(x)) = x. M is called locally projective if every epimorphism onto M is locally split. We prove that the following conditions are equivalent:(1) M is Zelmanowitz-regular.(2) every homomorphism into M...
Some epimorphic regular contexts.
Some Examples of Orders of Global Dimension Two.
Some module cohomological properties of Banach algebras
We find some relations between module biprojectivity and module biflatness of Banach algebras and and their projective tensor product . For some semigroups , we study module biprojectivity and module biflatness of semigroup algebras .
Some remarks on global dimensions for cotorsion pairs
Special biserial algebras with no outer derivations
Let A be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of A with coefficients in the bimodule A vanishes if and only if A is representation-finite and simply connected (in the sense of Bongartz and Gabriel), if and only if the Euler characteristic of Q equals the number of indecomposable non-uniserial projective-injective A-modules (up to isomorphism). Moreover, if this is the case, then all the higher Hochschild cohomology groups...
Splitting of Gysin extensions.