On the second homology of the Sch\"{u}tzenberger product of monoids

MELEK YAĞCI; LEYLA BUGAY; HAYRULLAH AYIK

Makale detayları

On the second homology of the Sch\"{u}tzenberger product of monoids

Yazarlar:

MELEK YAĞCI | LEYLA BUGAY | HAYRULLAH AYIK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2015 Vol.39 Issue 5, pp.763-772

Belge Tipi:

Makale

Yayın Tarihi:

12/2015

Belge Dili:

Türkçe

Document ID (Org No.):

2000747138

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

For two finite monoids SSS and TTT, we prove that the second integral homology of the Sch\"{u}tzenberger product S◊TS◊TS\Diamond T is equal to H2(S◊T)=H2(S)×H2(T)×(H1(S)⊗ZH1(T))H2(S◊T)=H2(S)×H2(T)×(H1(S)⊗ZH1(T))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◊TS◊TS\Diamond T is inefficient if there is no left or right invertible element in both SSS and TTT.

 

For two finite monoids SSS and TTT, we prove that the second integral homology of the Sch\"{u}tzenberger product S◊TS◊TS\Diamond T is equal to H2(S◊T)=H2(S)×H2(T)×(H1(S)⊗ZH1(T))H2(S◊T)=H2(S)×H2(T)×(H1(S)⊗ZH1(T))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◊TS◊TS\Diamond T is inefficient if there is no left or right invertible element in both SSS and TTT.

Makale detayları

On the second homology of the Sch\"{u}tzenberger product of monoids

Yazarlar:

MELEK YAĞCI | LEYLA BUGAY | HAYRULLAH AYIK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2015 Vol.39 Issue 5, pp.763-772

Belge Tipi:

Makale

Yayın Tarihi:

12/2015

Belge Dili:

Türkçe

Document ID (Org No.):

2000747138

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Monoid

Sch\"{u}tzenberger product

second integral homology

efficiency

Sayı

Makale detayları

On the second homology of the Sch\"{u}tzenberger product of monoids

Yazarlar: MELEK YAĞCI | LEYLA BUGAY | HAYRULLAH AYIK

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2015 Vol.39 Issue 5, pp.763-772

Belge Tipi: Makale

Yayın Tarihi: 12/2015

Belge Dili: Türkçe

Document ID (Org No.): 2000747138

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Monoid

Sch\"{u}tzenberger product

second integral homology

efficiency

Sayı

Yazarlar:

MELEK YAĞCI | LEYLA BUGAY | HAYRULLAH AYIK

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2015 Vol.39 Issue 5, pp.763-772

Belge Tipi:

Makale

Yayın Tarihi:

12/2015

Belge Dili:

Türkçe

Document ID (Org No.):

2000747138

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098