(Research Scholor) Bhagwant University Ajmer, Raj. (India)

Throughout this paper we have defined a new concept of almost
strongly M-flat modules11 and we are motivated10. And given several
properties of them13. This paper concept introduced as a generalization
of flat modules.
There are two part in discussion
In first part we study Almost strongly M-flat modules and in
second section we study about the homomorphism
( , )→ ( )
Where A is an R-algebra, XJ and NJ is R-modules.
And last result we prove M be almost strongly M-flat modules
then following statement are equivalent.
a) Any finitely generated ideal I is almost M-projective
b) Every submodule of M is almost strongly M-flat modules.
c) Every flat module is almost strongly M-flat module.