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Irreducible Subalgebra Primal Algebras

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Abstract

We present a characterisation of subalgebra primal algebras that are irreducible w.r.t. a localisation theory for finite algebras that replaces the role of polynomial operations and congruences in Tame Congruence Theory by term operations and arbitrary finitary compatible relations, respectively.

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References

  1. Behrisch, M.: Relational Tame Congruence Theory and Subalgebra Primal Algebras. Master’s thesis, TU Dresden [Dresden University of Technology] (2009). URL http://www.math.tu-dresden.de/~mbehri/documents/subalgebraPrimal_links.pdf

  2. Bergman, C.: Categorical equivalence of algebras with a majority term. Algebra Univers. 40(2), 149–175 (1998). URL citeseer.ist.psu.edu/bergman98categorical.html

    Google Scholar 

  3. Bergman, C., Berman, J.: Morita equivalence of almost-primal clones. J. Pure Appl. Algebra 108(2), 175–201 (1996). URL citeseer.ist.psu.edu/bergman94morita.html

    Google Scholar 

  4. Boercker, G.M.: Irreducible Sets in the Post Varieties. Master’s thesis, University of Louisville (2000)

  5. Clasen, M., Valeriote, M.: Tame congruence theory. In: Lectures on Algebraic Model Theory, Fields Inst. Monogr., vol. 15, pp. 67–111. American Mathematical Society, Providence (2002)

  6. Conaway, L., Kearnes, K.A.: Minimal sets in finite rings. Algebra Univers. 51(1), 81–109 (2004). doi:10.1007/s00012-004-1850-8

    Article  MathSciNet  MATH  Google Scholar 

  7. Foster, A.L.: Semi-primal algebras: characterization and normal-decomposition. Math. Z. 99, 105–116 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  8. Foster, A.L., Pixley, A.: Semi-categorical algebras. I. Semi-primal algebras. Math. Z. 83, 147–169 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hobby, D., McKenzie, R.: The structure of finite algebras. In: Contemporary Mathematics, vol. 76. American Mathematical Society, Providence (1988)

    Chapter  Google Scholar 

  10. Kearnes, K.A.: Tame Congruence Theory is a Localization Theory (2001). URL http://www.math.u-szeged.hu/confer/algebra/2001/lec+ex1.ps. Lecture Notes from “A Course in Tame Congruence Theory” Workshop, Budapest

  11. Moore, H.G., Yaqub, A.: An existence theorem for semi-primal algebras. Ann. Scuola Norm. Sup. Pisa (3) 22, 559–570 (1968)

    MathSciNet  MATH  Google Scholar 

  12. Yaqub, A.: Semi-primal categorical independent algebras. Math. Z. 93, 395–403 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zádori, L.: Relational sets and categorical equivalence of algebras. Int. J. Algebra Comput. 7(5), 561–576 (1997)

    Article  MATH  Google Scholar 

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  1. Institute of Algebra, Dresden University of Technology, 01062, Dresden, Germany

    Mike Behrisch

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  1. Mike Behrisch
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Correspondence to Mike Behrisch.

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Behrisch, M. Irreducible Subalgebra Primal Algebras. Order 29, 231–244 (2012). https://doi.org/10.1007/s11083-011-9220-6

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