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On the indecomposability of induced modules
1986
Journal of Algebra
Then v is indecomposable for every indecomposable direct summand W of SH. Moreover, if W, and W2 are two surh .summands, then WY z WF if and only 17 W, E W,. Remarks. (I ) If R = K, then the result is an easy consequence of Frobenius reciprocity; the proof given below, however, covers also this case. (2) A well known and much used special instance arises in case U = N. Condition (i) is then just that S is indecomposable, while (ii) asserts that HZ TJS). If R is a field, the theorem is therefore
doi:10.1016/0021-8693(86)90214-0
fatcat:copk6wgavzcodmeysgb64kf7qm