zbMATH — the first resource for mathematics

Modules in general algebra. (English) Zbl 0912.08001
Contributions to general algebra 10. Selection of lectures given at the conference on general algebra, Klagenfurt, Austria, May 29–June 1, 1997. Klagenfurt: Verlag Johannes Heyn. 41-53 (1998).
The author discusses structure theorems for Abelian algebras, which state that Abelian algebras are close to modules over rings. The highlights are Hermann’s Theorem stating that in congruence modular varieties Abelian algebras are affine, and Quackenbush’s Theorem characterizing quasi-affine algebras. Among other results it is shown that Hermann’s Theorem can be extended to any variety which satisfies a nontrivial lattice identity as a congruence equation.
For the entire collection see [Zbl 0889.00019].

08A05 Structure theory of algebraic structures