A higher version of Zappa products for monoids

Ahmet Sinan ÇEVİK; Suha WAZZAN; Fırat ATEŞ

doi:https://doi.org/10.15672/hujms.703437

Article Details

A higher version of Zappa products for monoids

Authors:

Ahmet Sinan ÇEVİK | Suha WAZZAN | Fırat ATEŞ

Publisher:

Hacettepe University

Main Topics:

Mathematics

Journal:

Hacettepe Journal of Mathematics and Statistics 2021 Vol.50 Issue 1, pp.224-234

Document Type:

Article

Publication Date:

2/2021

Document Language:

English

Document ID (Org No.):

2000450810

Frequency:

Bimonthly

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.703437

Abstract:

 

For arbitrary monoids AAA and BBB, a presentation for the restricted wreath product of AAA by BBB that is known as the semi-direct product of A⊕BA⊕BA^{\oplus B} by BBB has been widely studied. After that a presentation for the Zappa product of AAA by BBB was defined which can be thought as the mutual semidirect product of given these two monoids under a homomorphism ψ:A→T(B)ψ:A→T(B)\psi : A \rightarrow \mathcal{T}(B) and an anti-homomorphism δ:B→T(A)δ:B→T(A)\delta : B \rightarrow \mathcal{T}(A) into the full transformation monoid on BBB, respectively on AAA. As a next step of these above results, by considering the monoids A⊕BA⊕BA^{\oplus B} and B⊕AB⊕AB^{\oplus A}, we first introduce an extended version (generalization) of the Zappa product and then we prove the existence of an implicit presentation for this new product. Furthermore we present some other outcomes of the main theories in terms of finite and infinite cases, and also in terms of groups. At the final part of this paper we point out some possible future problems related to this subject.

Article Details

A higher version of Zappa products for monoids

Authors: Ahmet Sinan ÇEVİK | Suha WAZZAN | Fırat ATEŞ

Publisher: Hacettepe University

Main Topics: Mathematics

Journal: Hacettepe Journal of Mathematics and Statistics 2021 Vol.50 Issue 1, pp.224-234

Document Type: Article

Publication Date: 2/2021

Document Language: English

Document ID (Org No.): 2000450810

Frequency: Bimonthly

eISSN: 2651-477X

pISSN: 2651-477X

DOI: https://doi.org/10.15672/hujms.703437

Issues

Authors:

Ahmet Sinan ÇEVİK | Suha WAZZAN | Fırat ATEŞ

Publisher:

Hacettepe University

Main Topics:

Mathematics

Journal:

Hacettepe Journal of Mathematics and Statistics 2021 Vol.50 Issue 1, pp.224-234

Document Type:

Article

Publication Date:

2/2021

Document Language:

English

Document ID (Org No.):

2000450810

Frequency:

Bimonthly

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.703437