- Turkish Journal of Mathematics
- Vol: 39 Issue: 5
- On the second homology of the Sch"{u}tzenberger product of monoids
On the second homology of the Sch"{u}tzenberger product of monoids
Authors : Melek Yağci, Leyla Bugay, Hayrullah Ayik
Pages : 763-772
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Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :For two finite monoids $S$ and $T$, we prove that the second integral homology of the Sch\"{u}tzenberger product $S\Diamond T$ is equal to $$H_{2}(S\Diamond T)=H_{2}(S)\times H_{2}(T)\times (H_{1}(S)\otimes _{\mathbb Z} H_{1}(T)) $$ as the second integral homology of the direct product of two monoids. Moreover, we show that $S\Diamond T$ is inefficient if there is no left or right invertible element in both $S$ and $T$.Keywords : Monoid, Sch"{u}tzenberger product, second integral homology, efficiency