It is known that the bimodule derived mapping spaces between two operads have a delooping in terms of operadic space. We show relative version statement. The result has applications to disc embeddings fixed near boundary and framed embeddings.

let r and s be reduced rings with identities whose idempotents are central, and let m be an(r, s)-bimodule such that annr (m)=0. in this paper, we determine first the structure of automorphisms ofthe triangular ring, =sr mt0, and then, for all automorphisms α ,β of t we determine the structureof (α,β)-derivations of t.

We set up a fibred categorical theory of obstruction and classification morphisms that specialises to the one monoidal functors between groups also Schreier-Mac Lane group extensions. Further applications are provided crossed extensions bimodule butterflies, with in particular non-abelian unital associative algebras terms Hochschild cohomology.

The quiver Hopf algebras are classified by means of ramification system with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Hopf algebras of type one. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Hopf bimodule, Nichols algebras

In this paper, we establish the Pexiderized stability of coboundaries and cocycles and use them to investigate the Hyers–Ulam stability of some functional equations. We prove that for each Banach algebra A, Banach A-bimodule X and positive integer n,H(A,X) = 0 if and only if the n-th cohomology group approximately vanishes.

In this paper the Poincaré–Birkhoff–Witt (PBW) rings are characterized. Gröbner bases techniques are also developed for these rings. An explicit presentation of Exti (M,N) is provided when N is a centralizing bimodule. Mathematics Subject Classifications (2000): 16Z05, 16E30.

Abstract Let R and S be arbitrary rings let C S R {{}_{R}C_{S}} a semidualizing bimodule,

we investigate some properties of approximately quasi inner generalized dynamics and quasi approximately inner generalized derivations on modules. in particular, we prove that if a is a c*-algebra, is the generator of a generalized dynamics on an a-bimodule m satisfying and there exist two sequences of self adjoint elements in a such that for all in a core for , , then is approximately quasi in...