• Sumit Kumar Dekate

Abstract: Throughout this paper I have proved some results which are establishing the preservance of exactness property under change of ring. First of all If R and S are two rings such that M and M are two left modules then for a surjective homomorphism Ø: S → R, if M is exact then M is exact.Then I have established the converse of above result as : Let f:R→S be a surjective ring homomorphism and let M be an abelian group that is simultaneously a left R- module and a left S-module and if M is an exact module then M is exact. Later I have defined weakly exact module and with the result if M be any exact left R-module, M be any other module and f:R→ S be a homomorphism suppose M be a maximal submodule of M then M is weakly exact bimodule. At last I have the result that if M be any module of finite length and if for any n>0, M is exact then M is exact.

change of rings, homomorphism, surjective homomorphism, Balanced bimodules.

"Exact Modules under Change of Rings", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.11, Issue 11, page no.b361-b367, November-2024, Available :http://www.jetir.org/papers/JETIR2411147.pdf

"Exact Modules under Change of Rings", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.11, Issue 11, page no. ppb361-b367, November-2024, Available at : http://www.jetir.org/papers/JETIR2411147.pdf