Local P-Algebra

Let P be a class of (universal) algebras. Then an algebra A is a local P-algebra provided that every finitely generated subalgebra F of A is a member of the class P.

Note that classes P of algebras are identified with properties of algebras, so an algebra in the class P is said to be a P-algebra.

See also

Hyper-P Algebra

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

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Burris, S. and Sankappanavar, H. P. A Course in Universal Algebra. New York: Springer-Verlag, 1981., M.; Kaiser, K.; and Insall, M. "Some Nonstandard Methods Applied to Distributive Lattices." Zeitschrifte für Mathematische Logik und Grundlagen der Mathematik 36, 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.

Referenced on Wolfram|Alpha

Local P-Algebra

Cite this as:

Insall, Matt. "Local P-Algebra." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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