Abstract: In this paper we will show that
1. Every simple ring is exact.
2. If R be any simple ring then each direct summand of R and R is exact.
3. If R be any simple ring then any free left module over R is exact.
4. Let m, n N then for any simple ring R the bimodule Hom (R , R ) is exact left M (R) and right M (R) bimodule.
5. Let n N then for any simple ring R, End (R ) End (R )is exact.
6. For any simple ring R and any idempotent e in R, ReR≠0 is exact.
7. If R be any simple ring e be any idempotent in R then Hom (Re eR , R) and Hom (eR Re , R) are exact.
Throughout this paper we will consider that all rings have unity and all modules are unitary.
Keyword: Simple Ring, Direct summand, free left module, Bimodule, Exact module, Idempotent
Title: Generalization of Exactness on Simple Ring
Author: Dr. Sumit Kumar Dekate
International Journal of Mathematics and Physical Sciences Research
ISSN 2348-5736 (Online)
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