Jacobi–Zariski long nearly exact sequences for associative algebras

On split exact sequences Hopf algebras

Exact sequences of extended $d$-homology

In this article, we show the existence of certain exact sequences with respect to two homology theories, called d-homology and extended d-homology. We present sufficient conditions for the existence of long exact extended d- homology sequence. Also we give some illustrative examples.

REES SHORT EXACT SEQUENCES OF S-POSETS

In this paper the notion of Rees short exact sequence for S-posets is introduced, and we investigate the conditions for which these sequences are left or right split. Unlike the case for S-acts, being right split does not imply left split. Furthermore, we present equivalent conditions of a right S-poset P for the functor Hom(P;-) to be exact.

Identities of Associative Algebras

The structure theory for Pi-algebras is well developed. Some results of this theory are classic now. One of them is Kaplansky's theorem which asserts that a primitive Pi-algebra is finite dimensional over its centre. Another example is the theorem of Nagata-Higman which asserts that any algebra over a field of zero characteristic satisfying identity x" = 0 is nilpotent. In 1957 A.I. Shirshov pr...

Non Associative Linear Algebras