Open AccessOn the second homology of the Schützenberger product of monoids
Author(s) -
Melek Yağcı,
Leyla BUGAY,
Hayrullah Ayık
Publication year - 2015
Publication title -
turkish journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.454
H-Index - 27
eISSN - 1303-6149
pISSN - 1300-0098
DOI - 10.3906/mat-1503-79
Subject(s) - mathematics , invertible matrix , homology (biology) , diamond , product (mathematics) , pure mathematics , combinatorics , geometry , chemistry , biochemistry , organic chemistry , gene
For two finite monoids S and T , we prove that the second integral homology of the Schützenberger product S3T is equal to H2(S3T ) = 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 S3T is inefficient if there is no left or right invertible element in both S and T .
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