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algebra universalis

, 8:221 | Cite as

The subalgebra systems of direct powers

  • I. G. Rosenberg
Article

Abstract

A simple characterization of the subalgebra systems of direct powers of finitary universal algebras on a fixed infinite setA is given. For |I|≥|A| such subalgebra system of anI-power is precisely an algebraic closure systemS onA I closed under mutations ofI (which encompass both the precomposition by permutations ofI and allowing the values at specified elements ofI to become unrestricted) and such that each function in the intersection ofS is constant. For |I|<|A| the subalgebra systems ofI-powers are obtained as the restrictions toI of such closure systems on someA J withJI and |J|=|A|.

Keywords

Algebra UNIV Universal Algebra Direct Power Primal Algebra Polynomial Classis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag 1978

Authors and Affiliations

  • I. G. Rosenberg
    • 1
  1. 1.Université de MontréalMontréalCanada

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