Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 46, No. 1, pp. 71-102 (2005)
Linear extensions and nilpotence of Maltsev theories
Mamuka Jibladze and Teimuraz PirashviliDepartment of Algebra, Razmadze Mathematical Institute, Tbilisi 380093, Georgia
Abstract: Relationship is clarified between the notions of linear extension of algebraic theories, and central extension, in the sense of commutator calculus, of their models. Varieties of algebras turn out to be nilpotent Maltsev precisely when their theories may be obtained as results of iterated linear extensions by bifunctors from the so called abelian theories. The latter theories are described; they are slightly more general than theories of modules over a ring.
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Electronic version published on: 11 Mar 2005. This page was last modified: 4 May 2006.