Turkish Journal of Mathematics
DOI
10.3906/mat-1503-79
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
First Page
763
Last Page
772
Recommended Citation
YAĞCI, MELEK; BUGAY, LEYLA; and AYIK, HAYRULLAH
(2015)
"On the second homology of the Sch\"{u}tzenberger product of monoids,"
Turkish Journal of Mathematics: Vol. 39:
No.
5, Article 13.
https://doi.org/10.3906/mat-1503-79
Available at:
https://journals.tubitak.gov.tr/math/vol39/iss5/13
