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Bounded endomorphisms of free P-algebras

Published online by Cambridge University Press:  18 May 2009

Daniel Ševčovič
Daniel Ševčovič
Affiliation:
Department of Mathematical Analysis, Faculty of Mathematics and Physics, Comenius University, Mlynska Dolina, 842 15 Bratislava, Czechoslovakia
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The present note deals with bounded endomorphisms of free p-algebras (pseudocomplemented lattices). The idea of bounded homomorphisms was introduced by R. McKenzie in [8]. T. Katriňák [5] subsequently studied the properties of bounded homomorphisms for the varieties of p-algebras. This concept is also an efficient tool for the characterization of, so-called, splitting as well as projective algebras in the varieties of all lattices or p-algebras. For details the reader is referred to [2], [5], [6], [7] and other references therein. Let us emphasize that the main results that are contained in the above mentioned references strongly depend on the boundedness of each endomorphism of any finitely generated free algebra in a given variety.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 2 , May 1992 , pp. 209 - 214
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

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