TOPICS
Search

Strong Variety


A variety V of algebras is a strong variety provided that for each subvariety W of V, and each algebra A in V, if A is generated by its W- subalgebras, then A in W.

In strong varieties, sums of locally finite algebras are locally finite.


See also

Variety

This entry contributed by Matt Insall (author's link)

Explore with Wolfram|Alpha

References

Burris, S. and Sankappanavar, H. P. A Course in Universal Algebra. New York: Springer-Verlag, 1981. http://www.thoralf.uwaterloo.ca/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 Variety

Cite this as:

Insall, Matt. "Strong Variety." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/StrongVariety.html

Subject classifications