1D®f 8. Let 0 ABC-0 be a short exact sequence of left R-modules and D a right R-module. Then 0→DORA- DORBDOR C-0 is a short exact sequence of abelian groups under any one of the following hypotheses: (a) 0 ABC-0 is split exact. (b) R has an identity and D is a free right R-module. (c) R has an identity and D is a projective unitary right R-module.
1D®f 8. Let 0 ABC-0 be a short exact sequence of left R-modules and D a right R-module. Then 0→DORA- DORBDOR C-0 is a short exact sequence of abelian groups under any one of the following hypotheses: (a) 0 ABC-0 is split exact. (b) R has an identity and D is a free right R-module. (c) R has an identity and D is a projective unitary right R-module.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.8: Some Results On Finite Abelian Groups (optional)
Problem 14E: Suppose that the abelian group G can be written as the direct sum G=C22C3C3, where Cn is a cyclic...
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