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THE FUNDAMENTAL THEOREM OF CENTRAL ELEMENT THEORY

Part of: Model theory Varieties

Published online by Cambridge University Press:  07 September 2020

MARIANA VANESA BADANO  and
DIEGO JOSE VAGGIONE
MARIANA VANESA BADANO
Affiliation:
FACULTAD DE MATEMÁTICA, ASTRONOMÍA, FÍSICA Y COMPUTACIÓN UNIVERSIDAD NACIONAL DE CÓRDOBA CÓRDOBA 5000, ARGENTINAE-mail: marianabadano@hotmail.comE-mail: dvaggione@gmail.com
DIEGO JOSE VAGGIONE
Affiliation:
FACULTAD DE MATEMÁTICA, ASTRONOMÍA, FÍSICA Y COMPUTACIÓN UNIVERSIDAD NACIONAL DE CÓRDOBA CÓRDOBA 5000, ARGENTINAE-mail: marianabadano@hotmail.comE-mail: dvaggione@gmail.com
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Abstract

We give a short proof of the fundamental theorem of central element theory (see: Sanchez Terraf and Vaggione, Varieties with definable factor congruences, T.A.M.S. 361). The original proof is constructive and very involved and relies strongly on the fact that the class be a variety. Here we give a more direct nonconstructive proof which applies for the more general case of a first-order class which is both closed under the formation of direct products and direct factors.

Keywords

Boolean factor relationsdefinable factor relationscentral elementdirect productfactor congruence

MSC classification

Primary: 03C05: Equational classes, universal algebra
Secondary: 03C40: Interpolation, preservation, definability 08B25: Products, amalgamated products, and other kinds of limits and colimits
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 4 , December 2020 , pp. 1599 - 1606
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Copyright
© The Association for Symbolic Logic 2020

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References

REFERENCES

Bigelow, D. and Burris, S., Boolean algebras of factor congruences. Acta Scientiarum Mathematicarum, vol. 54 (1990), pp. 11–20.Google Scholar
Chang, C. C., Jónsson, B., and Tarski, A., Refinement properties for relational structures. Fundamenta Mathematicae, vol. 55 (1964), pp. 249–281.CrossRefGoogle Scholar
Comer, S., Representations by algebras of sections of Boolean spaces. Pacific Journal of Mathematics, vol. 38 (1971), pp. 29–38.CrossRefGoogle Scholar
Fell, J. and Tarski, A., On algebras whose factor algebras are Boolean. Pacific Journal of Mathematics, vol. 2 (1952), pp. 297–318.CrossRefGoogle Scholar
Jónsson, B. and Tarski, A., Direct Decompositions of Finite Algebraic Systems, University of Notre Dame, South Bend, IN, 1947.Google Scholar
Pierce, R., Modules Over Commutative Regular Rings, American Mathematical Society Memoirs, vol. 70, American Mathematical Society, Providence, RI, 1967.Google Scholar
Sanchez Terraf, P. and Vaggione, D., Varieties with definable factor congruences. Transactions of the American Mathematical Society, vol. 361 (2009), pp. 5061–5088.CrossRefGoogle Scholar
Tarski, A., Cardinal Algebras, Oxford University Press, New York, 1949.Google Scholar