Let
be a class of (universal) algebras. Then an algebra is a local -algebra provided that every finitely generated subalgebra of is a member of the class .
Note that classes
of algebras are identified with properties of algebras, so an algebra in the class
is said to be a -algebra.
Burris, S. and Sankappanavar, H. P. A Course in Universal Algebra. New York: Springer-Verlag, 1981. http://www.thoralf.uwaterloo.ca/htdocs/ualg.html.Gehrke,
M.; Kaiser, K.; and Insall, M. "Some Nonstandard Methods Applied to Distributive
Lattices." Zeitschrifte für Mathematische Logik und Grundlagen der Mathematik36,
123-131, 1990.Grätzer, G. Universal
Algebra, 2nd ed. New York: Springer-Verlag, 1979.Insall, M.
"Nonstandard Methods and Finiteness Conditions in Algebra." Zeitschr.
f. Math., Logik, und Grundlagen d. Math.37, 525-532, 1991.Insall,
M. "Some Finiteness Conditions in Lattices Using Nonstandard Proof Methods."
J. Austral. Math. Soc.53, 266-280, 1992.Kegel, O. H.
and Wehrfritz, B. A. F. Locally
Finite Groups. Amsterdam, Netherlands: North-Holland, 1973.Robinson,
D. J. S. Finiteness
Conditions and Generalized Soluble Groups, Parts 1 and 2. Berlin: Springer-Verlag,
1972.
be a class of (universal) algebras. Then an algebra 
is a local 
-algebra provided that every finitely generated subalgebra 
of 
is a member of the class 
.
of algebras are identified with properties of algebras, so an algebra in the class
is said to be a 
-algebra.
