# RELATIVE PROJECTIVITY AND RELATED RESULTS

• Toroghy, H.Ansari
• Published : 2004.08.01
• 58 10

#### Abstract

Let R be a commutative Noetherian ring and let M be an Artinian R-module. Let M${\subseteq}$M′ be submodules of M. Suppose F is an R-module which is projective relative to M. Then it is shown that $Att_{R}$($Hom_{A}$ (F,M′) :$Hom_{A}$(F,M) $In^n$), n ${\in}$N and $Att_{R}$($Hom_{A}$(F,M′) :$Hom_{A}$(F,M) In$^n$ $Hom_{A}$(F,M") :$Hom_{A}$(F,M) $In^n$),n ${\in}$ N are ultimately constant.

#### Keywords

associated primes;relative projectivity;attached primes

#### References

1. Frank W. Anderson and Kent R. Fuller, Categories of Modules (second edition), Springer-Verlag, New York, 1992