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The book "A Course in Constructive Algebra" (1988) shows the way ofunderstanding classical basic algebra in a constructive style similar toBishop's Constructive Mathematics. Classical theorems are revisited, with a newflavour, and become much more precise. We are often surprised to find proofsthat are simpler and more elegant than the usual ones. In fact, when one cannotuse magic tools as the law of excluded middle, it is necessary to understandwhat is the true content of a classical proof. Also, usual shortcuts allowed inclassical proofs introduce sometimes useless detours. In order to understandclearly a problem, prescience may be a handicap.

Algebra in Bishop's style: some major features of the book "A Course in Constructive Algebra'' by Mines, Richman, and Ruitenburg