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On Polynomial Algebras and Free Algebras

Published online by Cambridge University Press:  20 November 2018

George Grätzer
George Grätzer*
Affiliation:
The Pennsylvania State University, University Park, Pennsylvania; The University of Manitoba, Winnipeg, Manitoba
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It is well known that given the polynomial algebra (for definitions, see §2), an algebra of type τ, and a sequence a of elements of , one can define a congruence relation θa of such that the factor algebra is isomorphic to the subalgebra of generated by a, and the isomorphism is given in a very simple way.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 575 - 581
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

Research supported by the National Science Foundation under grant number GP-4221. Theorem 1 was announced in Notices Amer. Math. Soc, 12 (1965), 336.

References

1. Birkhoff, G., On the structure of abstract algebras, Proc. Cambridge Philos. Soc, 81 (1935), 433–454.Google Scholar
2. Gratzer, G. and Schmidt, E. T., Characterizations of congruence lattices of abstract algebras, Acta. Sci. Math. (Szeged), 24 (1963), 34–59.Google Scholar
3. Sikorski, R., Products of abstract algebras, Fund. Math., 89 (1952), 211–228.Google Scholar