(R, S)-Modules and (1, k)-Jointly Prime (R, S)-Submodules

We introduced the notions of (1, k)-prime ideal and (1, k)-jointly prime (R, S)-submodule as a generalization of prime ideal and jointly prime (R, S)-submodule, respectively. We provide a relationship between (1, k)-prime ideal and (1, k)-jointly prime (R, S)-submodule. Characterizations of (1, k)-jointly prime (R, S)- submodules are also given.

• Thawatchai Khumprapussorn

• R
• S)-module
• (1
• k)-prime ideal
• (1
• k)-jointly prime (R
• S)-submodule.

<p>[1] T. Khumprapussorn, S. Pianskool and M. Hall, (R, S)-modules and Their
Fully prime and Jointly prime Submodules, IMF, 7 (2012), 1631 - 1643.
[2] T. Khumprapussorn, Left R-prime(R, S)-submodules, IMF, 8 (2013), 619
- 626.</p>