the generalized total graph of modules respect to proper submodules over commutative rings.

let $m$ be a module over a commutative ring $r$ and let $n$ be a proper submodule of $m$. the total graph of $m$ over $r$ with respect to $n$, denoted by $t(gamma_{n}(m))$, have been introduced and studied in [2]. in this paper, a generalization of the total graph $t(gamma_{n}(m))$, denoted by $t(gamma_{n,i}(m))$ is presented, where $i$ is an ideal of $r$. it is the graph with all elements of $m$ as vertices, and for distinct $m,nin m$, the vertices $m$ and $n$ are adjacent if and only if $m+nin m(n,i)$, where $m(n,i)={min m : rmin n+im for some rin r-i}$. the main purpose of this paper is to extend the definitions and properties given in [2] and [12] to a more general case.