Leyla BUĞAY, Hayrullah AYIK, Melek YAGCI

On the second homology of the Sch¨utzenberger product of monoids

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

For two finite monoids S and T , we prove that the second integral homology of the Sch¨utzenberger product S✸T is equal to H2(S✸T) = H2(S) × H2(T) × (H1(S) ⊗Z H1(T)) as the second integral homology of the direct product of two monoids. Moreover, we show that S✸T is inefficient if there is no left or right invertible element in both S and T .

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[1] Ayık H, Campbell CM, OConnor JJ, Ruskuc N. Minimal presentations and efficiency of semigroups. Semigroup Forum 2000; 60: 231242.
[2] Ayık H, Campbell CM, OConnor JJ, Ruskuc N. On the efficiency of finite simple semigroups. Turk J Math 2000; 24: 129146.
[3] Ayık H, Campbell CM, OConnor JJ. On the efficiency of the direct products of Monogenic Monoids. Algebra Colloq 2007; 14: 279284.
[4] Campbell CM, Mitchell JD, Ruskuc N. On defining groups efficiently without using inverses. Math P Camb Phil Soc 2002; 133: 3136.
[5] C¸ evik AS. Minimal but inefficient presentations of the semi-direct products of some monoids. Semigroup Forum 2003; 66: 117.
[6] C¸ evik AS. The p-Cockcroft property of the semi-direct products of monoids. Int J Algebra Comput 2003; 13: 116.
[7] Guba VS, Pride SJ. Low dimensional (co)homology of free Burnside monoids. J Pure Appl Algebra 1996; 108: 6179.
[8] Guba VS, Pride SJ. On the left and right cohomological dimension of monoids. Bull London Math Soc 1998; 30: 391396.
[9] Howie JM. Fundamentals of Semigroup Theory. New York, NY, USA: Oxford University Press, 1995.
[10] Howie JM, Ruskuc N. Constructions and presentations for monoids. Comm Algebra 1994; 49: 62096224.
[11] Johnson DL. Presentations of Groups. Cambridge, UK: Cambridge University Press, 1990.
[12] Squier C. Word problems and a homological finiteness condition for monoids. J Pure Appl Algebra 1987; 49: 201217.