Document Type : Original Manuscript


1 Department of Mathematics, University of Farhangian, Tehran, Iran.

2 Department of Mathematics, University of Shahid Beheshti, Tehran, Iran.


In the present paper, by considering the notion of
MV-modules which is the structure that naturally correspond
to lu-modules over lu-rings, we prove some results on prime A-ideals and state some conditions to obtain a prime A-ideal in MV-modules. Also, we state some conditions that an A-ideal is not prime and investigate conditions that $K\subseteq \bigcup _{i=1}^{n}K_{i}$ implies $K\subseteq K_{j}$, where $K,K_{1},\cdots ,K_{n}$ are A-ideals of A-module M and $1\leq j\leq n$.