A variety 
of algebras is a strong variety provided that for each subvariety 
of 
, and each algebra 
, if 
is generated by its 
- subalgebras, then 
.
In strong varieties, sums of locally finite algebras are locally finite.
Strong Variety
See also
VarietyThis entry contributed by Matt Insall (author's link)
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References
Burris, S. and Sankappanavar, H. P. A Course in Universal Algebra. New York: Springer-Verlag, 1981. https://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html.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.Referenced on Wolfram|Alpha
Strong VarietyCite this as:
Weisstein, Eric W., with contributions by Matt Insall. "Strong Variety." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/StrongVariety.html