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Cohomology monoids of monoids with coefficients in semimodules II

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Abstract

We relate the old and new cohomology monoids of an arbitrary monoid M with coefficients in semimodules over M, introduced in the author’s previous papers, to monoid and group extensions. More precisely, the old and new second cohomology monoids describe Schreier extensions of semimodules by monoids, and the new third cohomology monoid is related to a certain group extension problem.

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Acknowledgements

I would like to thank the referee for valuable comments.

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Correspondence to Alex Patchkoria.

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Communicated by László Márki.

This work was supported by Shota Rustaveli National Science Foundation Grant DI/18/5-113/13.

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Patchkoria, A. Cohomology monoids of monoids with coefficients in semimodules II. Semigroup Forum 97, 131–153 (2018). https://doi.org/10.1007/s00233-017-9900-7

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  • DOI: https://doi.org/10.1007/s00233-017-9900-7

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