Prime–Extending Module and S-Prime Module

Authors

  • Tamadher A Ibrahiem Department of Mathematics, College of Science for Women, University of Baghdad, Iraq.

Keywords:

Extending module, Prime –Extending module, Prime direct summand, Prime submodule, uniform submodule

Abstract



In this paper, the notation of prime-extending module, is introduced and studied where an R-module M is Prime-extending if every nonzero proper submodule of M is essential in prime direct summand .Beside these, the notation of S-prime is given, where an R module is called S-prime if every proper direct summand is prime for this notation we proved: 1.Under the condition of S-prime module, M is Prime-extending if and only if M is extending .2. If M is semisimple module, then M is Prime-extending if and only if M is S-prime.

 

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Published

2011-12-01

Issue

Vol. 14 No. 4 (2011): December

Section

Articles

How to Cite

[1]
“Prime–Extending Module and S-Prime Module”, ANJS, vol. 14, no. 4, pp. 166–170, Dec. 2011, Accessed: May 02, 2024. [Online]. Available: https://anjs.edu.iq/index.php/anjs/article/view/782