ON S-EXTENDING MODULES

Year 2020, Volume: 27 Issue: 27, 102 - 113, 07.01.2020

Manar E. Tabarak M. A. Kamal M. H. Elbaroudy Salah El Din S. Hussien

https://doi.org/10.24330/ieja.662972

Abstract

Here we introduce and study the concept of relative superfluous injectivity, which is a generalization of relative injectivity. We show some of the properties that hold true for relative injectivity still hold for relative superfluous injectivity. We also introduce and characterize the new concept of superfluous extending modules. Finally, we make use of relative superfluous injectivity to study direct sums of superfluous extending modules.

Keywords

superfluous injective module, large submodule, superfluous extending module

References

• F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Second edition, Graduate Texts in Mathematics, 13, Springer-Verlag, New York, 1992.
• W. D. Burgess and R. Raphael, On modules with the absolute direct summand property, Ring Theory (Granville, OH, 1992), World Sci. Publ., River Edge, NJ, (1993), 137-148.
• H. Q. Dinh, A note on pseudo injective modules, Comm. Algebra, 33(2) (2005), 361-369.
• N. V. Dung, D. V. Huynh, P. F. Smith and R. Wisbaur, Extending Modules, with the collaboration of John Clark and N. Vanaja, Pitman Research Notes in Mathematics Series, 313, Longman Scientic & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1994.
• M. A. Kamal and B. J. Muller, Extending modules over commutative domains, Osaka J. Math., 25(3) (1988), 531-538.
• E. Mermut, C. Santa-Clara and P. F. Smith, Injectivity relative to closed sub- modules, J. Algebra, 321(2) (2009), 548-557.
• M. Okado, On the decomposition of extending modules, Math. Japon., 29(6) (1984), 939-941.
• M. F. Yousif and Y. Zhou, FP-injective, simple-injective, and quasi-Frobenius rings, Comm. Algebra, 32(6) (2004), 2273-2285.