Every vector space over a division ring Dis both a projective and an injective D-module. [See Exercise
Question:
Every vector space over a division ring Dis both a projective and an injective D-module. [See Exercise 1.]
Data from exercise 1
The following conditions on a ring R [with identity] are equivalent:
(a) Every [unitary] R-module is projective.
(b) Every short exact sequence of [unitary] R-modules is split exact.
(c) Every [unitary] R-module is injective.
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Related Book For 
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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