SS-Injective Modules and Rings

Authors

  • Akeel Ramadan Mehdi Department of Mathematics, College of Education, University of Al-Qadisiyah
  • Adel Salim Tayyah Department of Mathematics ,College of Computer science and Information Technology ,University of AL-Qadisiya

DOI:

https://doi.org/10.29304/jqcm.2017.9.2.296

Keywords:

Small Injective rings (modules); Soc-Injective rings (modules); SS-Injective rings (modules); Perfect rings; quasi-Frobenius rings.

Abstract

     We introduce and investigate SS-injectivity as a generalization of both soc-injectivity and small injectivity. A right module  over a ring  is said to be SS- -injective (where  is a right -module) if every -homomorphism from a semisimple small submodule of  into  extends to . A module  is said to be SS-injective (resp. strongly SS-injective), if  is SS- -injective (resp. SS- -injective for every right -module ). Some characterizations and properties of (strongly) SS-injective modules and rings are given. Some results on soc-injectivity are extended to SS-injectivity.

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Published

2017-11-15

How to Cite

Ramadan Mehdi, A., & Salim Tayyah, A. (2017). SS-Injective Modules and Rings. Journal of Al-Qadisiyah for Computer Science and Mathematics, 9(2), Math 57–70. https://doi.org/10.29304/jqcm.2017.9.2.296

Issue

Vol. 9 No. 2 (2017): JQCM

Section

Math Articles