Novikov, Boris V.; Polyakova, Lyudmyla Yu. On 0-homology of categorical at zero semigroups. (English) Zbl 1182.20059 Cent. Eur. J. Math. 7, No. 2, 165-175 (2009). Summary: 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. Cited in 1 Document MSC: 20M50 Connections of semigroups with homological algebra and category theory 18G60 Other (co)homology theories (MSC2010) Keywords:homology of semigroups; 0-homology of semigroups; categorical at zero semigroups PDF BibTeX XML Cite \textit{B. V. Novikov} and \textit{L. Yu. Polyakova}, Cent. Eur. J. Math. 7, No. 2, 165--175 (2009; Zbl 1182.20059) Full Text: DOI References: [1] Adyan S.I., Defining relations and algorithmical problems for groups and semigroups, Tr. Mat. Inst. Steklova, 1966, 85 (in Russian) · Zbl 0204.01702 [2] Cartan H., Eilenberg S., Homological algebra, Princeton University Press, Princeton, N.J., 1956 [3] Clifford A.H., Preston G.B., The algebraic theory of semigroups II, Mathematical Surveys, No. 7, American Mathematical Society, Providence, 1967 · Zbl 0178.01203 [4] Dehornoy P., Lafont Yv., Homology of Gaussian groups, Ann. Inst. Fourier, 2003, 53(2), 489-540 · Zbl 1100.20036 [5] Husainov A.A., On the homology of small categories and asynchronous transition systems, Homology Homotopy Appl., 2004, 6(1), 439-471 · Zbl 1078.18005 [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 [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-R [8] MacLane S., Categories for the working mathematician, Springer-Verlag, New York-Heidelberg-Berlin, 1972 · Zbl 0705.18001 [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) [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) · Zbl 0543.20052 [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 · Zbl 0994.20049 [12] Polyakova L.Yu., On 0-homology of semigroups, preprint · Zbl 1164.20370 [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)90129-0 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.