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Envelopes and covers in the theory of modules. (English) Zbl 1051.16004
In 1999, one of the well-known problems about approximations, the Flat Cover Conjecture, was solved with an essential contribution of Czech mathematicians (the author and L. Bican). The author presents an outline of the theory of modules and their covers, of methods used in the proof of the FCC and of their applications. The paper was published on the occasion of the World Mathematical Year 2000.

16D40 Free, projective, and flat modules and ideals in associative algebras
16D50 Injective modules, self-injective associative rings
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