On np-injective rings and Modules

Authors

  • Ferman A. Ahmed Department of Mathematics, College of Science, Salahaddin University-Erbil, Kurdistan Region - Iraq.
  • Abdullah M. Abdul-Jabbar Department of Mathematics, College of Science, Salahaddin University-Erbil, Kurdistan Region - Iraq.

DOI:

https://doi.org/10.15379/ijmst.v10i3.3110

Keywords:

Np-Injective, Trivial Extention, Non-Nilpotent Element, Annihilator,R-Modules.

Abstract

A given R-module  is called a right np-injective module if for any non-nilpotent element  of , and any right R-homomorphism  can be extended to , if  is np-injective, then  is a right np-injective ring. A given ring  is called right weakly np-injective if for each non-nilpotent element  of , there exists a positive integer  such that any right R-homomorphism  can be extended to . A given ring  is a right weakly np-injective ring, if . In the matrix ring, we poved that  is right np-injective, for some , if  is right Weakly np-injective. So, We extended many of the known properties and characterizations of right np-injective rings and modules. Finally, the main result in np-injective module found that the R-module  is np-injective module if and only if for any  the short exact sequence  of R-modules,  is also a short exact sequence, where  and .

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Published

2023-06-13

How to Cite

[1]
F. A. Ahmed and A. M. . Abdul-Jabbar, “On np-injective rings and Modules”, ijmst, vol. 10, no. 3, pp. 3149-3159, Jun. 2023.