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The commutative cohomology of nilmonoids, revisited

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Abstract

A nilmonoid is a nilsemigroup N with an identity element adjoined. New properties of the canonical presentation of N yield a more precise characterization of 2-cocycles, improvements in the computation of the cohomology of N, and a universal coefficients theorem.

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References

  1. Eilenberg, S., MacLane, S.: Relations between homology and homotopy groups. Proc. Natl. Acad. Sci. USA 29, 155–158 (1943)

    Article  MathSciNet  Google Scholar 

  2. Grillet, P.A.: Left coset extensions. Semigroup Forum 7, 200–263 (1974)

    Article  MathSciNet  Google Scholar 

  3. Grillet, P.A.: The commutative cohomology of nilsemigroups. J. Pure Appl. Algebra 82, 233–251 (1992)

    Article  MathSciNet  Google Scholar 

  4. Grillet, P.A.: A short proof of Rédei’s theorem. Semigroup Forum 46, 126–127 (1993)

    Article  MathSciNet  Google Scholar 

  5. Grillet, P.A.: The commutative cohomology of finite semigroups. J. Pure Appl. Algebra 102, 25–47 (1995)

    Article  MathSciNet  Google Scholar 

  6. Grillet, P.A.: Partially free commutative semigroups. Acta Sci. Math. (Szeged) 61, 155–169 (1995)

    MathSciNet  MATH  Google Scholar 

  7. Grillet, P.A.: Commutative Semigroups, Springer, Berlin (2001)

  8. Grillet, P.A.: Commutative nilsemigroup s with zero cohomology. Semigroup Forum 62, 66–78 (2001)

    Article  MathSciNet  Google Scholar 

  9. Leech, J.: \({\cal{H}}\)-coextension s of monoids. Mem. Am. Math. Soc. 157, 1–66 (1975)

    MathSciNet  Google Scholar 

  10. MacLane, S.: Homology, Springer, Berlin (1963)

    Book  Google Scholar 

  11. Rédei, L.: Die Verallgemeinerung der Schreierchen Erweiterungstheorie. Acta Sci. Math. (Szeged) 14, 252–273 (1952)

    MathSciNet  MATH  Google Scholar 

  12. Rosales, J.C.: Function minimum associated to a congruence on integral n-tuple space. Semigroup Forum 51, 87–95 (1995)

    Article  MathSciNet  Google Scholar 

  13. Weibel, C.A.: An Introduction to Homological Algebra, Cambridge University Press, Cambridge (1994)

    Book  Google Scholar 

Download references

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Authors and Affiliations

  1. Cape Canaveral, USA

    Pierre Antoine Grillet

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  1. Pierre Antoine Grillet
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Correspondence to Pierre Antoine Grillet.

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Communicated by Victoria Gould.

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Grillet, P.A. The commutative cohomology of nilmonoids, revisited. Semigroup Forum 101, 654–679 (2020). https://doi.org/10.1007/s00233-020-10107-4

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  • DOI: https://doi.org/10.1007/s00233-020-10107-4

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