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.

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.

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 we address the problem of characterizing the RNA complement of a given cell type, that is, the set of RNA species and their relative copy number, from a large set of short sequence reads which have been randomly sampled from the cell’s RNA sequences through a sequencing experiment. We refer to this problem as the transcriptome reconstruction problem, and we specifically investigat...

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.

(1.1) 0 −→ N f −−→M g −−→ P −→ 0 which is exact at N , M , and P . That means f is injective, g is surjective, and im f = ker g. Example 1.1. For an R-module M and submodule N , there is a short exact sequence 0 // N // M // M/N // 0, where the map N →M is the inclusion and the map M →M/N is reduction modulo N . Example 1.2. For R-modules N and P , the direct sum N ⊕ P fits into the short exact...