Document Type: Original Manuscript


1 Department of Pure Mathematics, Faculty of Mathematical Science, University of Guilan, P.O. Box 41335-19141, Rasht, Iran.

2 Department of Mathematics, Bandar Anzali Branch, Islamic Azad University, Ban- dar Anzali, Iran.


Let $R$ be a commutative ring with identity. The purpose of this paper is to introduce and study two classes of modules over $R$, called $\mbox{Max}$-injective and $\mbox{Max}$-strongly top modules and explore some of their basic properties. Our concern is to extend some properties of $X$-injective and strongly top modules to these classes of modules and obtain some related results.