this text carries out some ideas about exact and p− exact sequences of transformationsemigroups. some theorems like the short five lemma (lemma 1.3 and lemma 2.3) are valid here as inexact sequences of r − modules.

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.

The notion of quasi-exact sequence of modules was introduced by B. Davvaz and coauthors in 1999 as a generalization of the notion of exact sequence. In this paper we investigate further this notion. In particular, some interesting results concerning this concept and torsion functor are given.

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.

In this paper we introduce a new definition of the first non-abelian cohomology of topological groups.  We relate the cohomology of a normal subgroup $N$ of a topological group $G$ and the quotient $G/N$ to the cohomology of $G$. We get the inflation-restriction exact sequence. Also, we obtain a seven-term exact cohomology sequence up to dimension 2. We give an interpretation of the first non-a...

The notion of the sub-exact sequence is generalization exact in algebra especially on a module. A module over ring R vector space field F. Refers to special F when we have complete inner product space, it called Hilbert space. if every Cauchy converges. Now, introduce which can later be useful statistics. This paper aims investigate properties and their relation direct summand As result, get tw...