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Implicit operations on the categories of universal algebras

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Abstract

We present a series of concepts and prove some results on implicit operations on the various categories of universal algebras. This generalizes the previous results for pseudovarieties, pseudouniversal classes of algebras, positively conditional pseudovarieties, and so on.

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References

  1. Eilenberg S. and Schützenbérger M. P., “On pseudovarieties,” Adv. Math., 19, No. 3, 413–418 (1976).

    Article  MATH  Google Scholar 

  2. Reiterman J., “The Birkhoff theorem for finite algebras,” Algebra Univ., 14, No. 1, 1–10 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  3. Higgins P. M., “An algebraic proof that pseudovarieties are defined by pseudoidentities,” Algebra Univ., 274, 597–599 (1990).

    Article  MATH  MathSciNet  Google Scholar 

  4. Pinus A. G., “On the implicit conditional operations defined on pseudouniversal classes,” Fund. Prikl. Mat., 10, No. 4, 171–182 (2004).

    MATH  MathSciNet  Google Scholar 

  5. Pinus A. G., “Positively conditional pseudovarieties and implicit operations on them,” Siberian Math. J., 47, No. 2, 307–314 (2006).

    Article  MathSciNet  Google Scholar 

  6. Pinus A. G., “∃+-conditional varieties, ∃+-conditional pseudovarieties, and implicit operations on them,” in: Algebra and Model Theory. 5 [in Russian], Novosibirsk State Technical Univ., Novosibirsk, 2005, pp. 138–161.

    Google Scholar 

  7. Pinus A. G., “On conditional terms and identities on universal algebras,” Vychisl. Sistemy, 156, 59–78 (1996).

    MathSciNet  Google Scholar 

  8. Pinus A. G., “Inner homomorphisms and positively conditional terms,” Algebra and Logic, 40, No. 2, 87–95 (2001).

    Article  MathSciNet  Google Scholar 

  9. Pinus A. G., “On functions commuting with semigroups of transformations of algebras,” Siberian Math. J., 41, No. 6, 1166–1173 (2000).

    Article  MathSciNet  Google Scholar 

  10. Pinus A. G., Conditional Terms and Their Applications to Algebra and the Theory of Computations [in Russian], Novosibirsk State Technical Univ., Novosibirsk (2002).

    Google Scholar 

  11. Pinus A. G., “Conditional terms and their applications in algebra and computation theory,” Russian Math. Surveys, 56, No. 4, 649–686 (2001).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Novosibirsk State Technical University, Novosibirsk, Russia

    A. G. Pinus

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  1. A. G. Pinus
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Correspondence to A. G. Pinus.

Additional information

Original Russian Text Copyright © 2009 Pinus A. G.

The author was supported by the Russian Foundation for Basic Research (Grant 06-01-00159-a).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 1, pp. 146–153, January–February, 2009.

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Pinus, A.G. Implicit operations on the categories of universal algebras. Sib Math J 50, 117–122 (2009). https://doi.org/10.1007/s11202-009-0014-7

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  • DOI: https://doi.org/10.1007/s11202-009-0014-7

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