Nearly Injective Semimodules

Abstract

An injectivity in the category of semimodules over semiring was studied by many authors recently. On the other hand, the concept of injectivity, in the category of modules over ring, was generalized in many different directions. In particular, injective modules relative to preradical were some of those generalizations.
 As an analogue to module theory, in this paper, we introduce and investigate the notion of "injective semimodule relative to Jacobson radical (namely nearly injective semimodule)".

التوليف والدراسة الطيفية لرباط رباعي رباعي جديد Azo-Azomethine كمركب لـ 4،5-diphenyl Imidazole ومجمعاته مع بعض الأيونات المعدنية

“…The mass spectra can be used to confirm the suggested structure of both ligand and it's complexes , the molecular ion of ligand appeared at(e/z =893) corresponding to the molecular formula ( C 54 H 48 N 14 ) , while the base peak appeared in ( e/z= 220) corresponding to 4,5-diphenylimidazole fragment ( C 15 H 12 N 2 ) (21) , The molecular peak of Ni(II) complex appeared in (e/z= 1022) with low m/z ( less 1%) due to the large Mwt. of ligand corresponding to the [(NiC 54 H 48 N 14 ) -Cl 2 ] fragment and the base peak in (e/z= 220) which is related to [( C 15 H 12 N 2 ) ] fragment , The successive fragmentation of ligand and it's complex with Ni (II) ion were show in schemes ( 4) and ( 5) , while mass spectra of them shown in the figures ( 4) and ( 5) Ph Ph…”

Almost Injective Semimodules

“…As regards semimodule, in 1998 Huda Althani gaves an equivalent definition of injective semimodules, which reduces to that in ISSN: 0067-2904 module theory. Also she studied some characterization of injective semimodules [3], later other authors discussed some generalizations of injective semimodules [4 ], [ 5] and [6]. In this work, the concept of injective semimodule has been extended to generalization, almostinjective semimodule.…”