Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

IMPACT FACTOR 2018: 0.726
5-year IMPACT FACTOR: 0.869

CiteScore 2018: 0.90

SCImago Journal Rank (SJR) 2018: 0.323
Source Normalized Impact per Paper (SNIP) 2018: 0.821

Mathematical Citation Quotient (MCQ) 2018: 0.34

ICV 2017: 161.82

Open Access
See all formats and pricing
More options …
Volume 7, Issue 2


Volume 13 (2015)

On 0-homology of categorical at zero semigroups

Boris Novikov / Lyudmyla Polyakova
Published Online: 2009-05-24 | DOI: https://doi.org/10.2478/s11533-009-0001-z


The isomorphism of 0-homology groups of a categorical at zero semigroup and homology groups of its 0-reflector is proved. Some applications of 0-homology to Eilenberg-MacLane homology of semigroups are given.

MSC: 20M50

Keywords: Homology of semigroups; 0-homology of semigroups; Categorical at zero semigroup

  • [1] Adyan S.I., Defining relations and algorithmical problems for groups and semigroups, Tr. Mat. Inst. Steklova, 1966, 85 (in Russian) Google Scholar

  • [2] Cartan H., Eilenberg S., Homological algebra, Princeton University Press, Princeton, N.J., 1956 Google Scholar

  • [3] Clifford A.H., Preston G.B., The algebraic theory of semigroups II, Mathematical Surveys, No. 7, American Mathematical Society, Providence, 1967 Google Scholar

  • [4] Dehornoy P., Lafont Yv., Homology of Gaussian groups, Ann. Inst. Fourier, 2003, 53(2), 489–540 Google Scholar

  • [5] Husainov A.A., On the homology of small categories and asynchronous transition systems, Homology Homotopy Appl., 2004, 6(1), 439–471 Google Scholar

  • [6] Husainov A.A., Tkachenko V.V., Asynchronous transition systems homology groups, In: Mathematical modeling and the near questions of mathematics. Collection of the scientifcs works, KhGPU, Khabarovsk, 2003, 23–33 Google Scholar

  • [7] Kobayashi Yu., Complete rewriting systems and homology of monoid algebras, J. Pure Appl. Algebra, 1990, 65, 263–275 http://dx.doi.org/10.1016/0022-4049(90)90106-RCrossrefGoogle Scholar

  • [8] MacLane S., Categories for the working mathematician, Springer-Verlag, New York-Heidelberg-Berlin, 1972 Google Scholar

  • [9] Novikov B.V., 0-cohomology of semigroups, In: Theoretical and applied questions of differential equations and algebra, Naukova Dumka, Kiev, 1978, 185–188 (in Russian) Google Scholar

  • [10] Novikov B.V., Defining relations and 0-modules over semigroup, Theory of semigroups and its applications, Saratov. Gos. Univ., Saratov, 1983, 116, 94–99 (in Russian) Google Scholar

  • [11] Novikov B.V., Semigroup cohomology and applications, Algebra — representation theory (Constanta, 2000), 219–234, NATO Sci. Ser. II Math. Phys. Chem., 28, Kluwer Acad. Publ., Dordrecht, 2001 Google Scholar

  • [12] Polyakova L.Yu., On 0-homology of semigroups, preprint Google Scholar

  • [13] Squier C., Word problem and a homological finiteness condition for monoids, J. Pure Appl. Algebra, 1987, 49, 201–217 http://dx.doi.org/10.1016/0022-4049(87)90129-0CrossrefGoogle Scholar

About the article

Published Online: 2009-05-24

Published in Print: 2009-06-01

Citation Information: Open Mathematics, Volume 7, Issue 2, Pages 165–175, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-009-0001-z.

Export Citation

© 2009 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Laurent Poinsot, Gérard H. E. Duchamp, and Christophe Tollu
Semigroup Forum, 2010, Volume 81, Number 3, Page 446

Comments (0)

Please log in or register to comment.
Log in