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2009 | 7 | 2 | 165-175
Tytuł artykułu

On 0-homology of categorical at zero semigroups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
2
Strony
165-175
Opis fizyczny
Daty
wydano
2009-06-01
online
2009-05-24
Twórcy
  • Department of Mechanics and Mathematics, Kharkov V.N. Karazin National University, Kharkov, Ukraine, pomilka@ukr.net
Bibliografia
  • [1] Adyan S.I., Defining relations and algorithmical problems for groups and semigroups, Tr. Mat. Inst. Steklova, 1966, 85 (in Russian)
  • [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
  • [4] Dehornoy P., Lafont Yv., Homology of Gaussian groups, Ann. Inst. Fourier, 2003, 53(2), 489–540
  • [5] Husainov A.A., On the homology of small categories and asynchronous transition systems, Homology Homotopy Appl., 2004, 6(1), 439–471
  • [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[Crossref]
  • [8] MacLane S., Categories for the working mathematician, Springer-Verlag, New York-Heidelberg-Berlin, 1972
  • [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)
  • [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
  • [12] Polyakova L.Yu., On 0-homology of semigroups, preprint
  • [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[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0001-z
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