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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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Projective but not free (exercise from Adkin - Weintraub) [closed]
This is exercise 38 from Chapter 3. Modules and Vector Spaces in Algebra by Adkins and Weintraub (GTM). How do you solve this problem?
Let
\begin{equation*}
R = \lbrace f : [0, 1] \to \Re : f \;\te …