On Idempotent Units in Commutative Group Rings

Ömer KÜSMÜŞ

doi:https://doi.org/10.16984/saufenbilder.733935

Makale detayları

On Idempotent Units in Commutative Group Rings

Yazarlar:

Ömer KÜSMÜŞ

Ana Başlıklar:

Matematik

Dergi:

Sakarya University Journal of Science 2020 Vol.24 Issue 4, pp.782-790

Belge Tipi:

Makale

Yayın Tarihi:

7/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000556787

DOI:

https://doi.org/10.16984/saufenbilder.733935

Özet:

 

Special elements as units, which are defined utilizing idempotent elements, have a very crucial place in a commutative group ring. As a remark, we note that an element is said to be idempotent if r^2=r in a ring. For a group ring RG, idempotent units are defined as finite linear combinations of elements of G over the idempotent elements in R or formally, idempotent units can be stated as of the form id(RG)={∑_(r_g∈id(R))▒〖r_g g〗: ∑_(r_g∈id(R))▒r_g =1 and r_g r_h=0 when g≠h} where id(R) is the set of all idempotent elements  [3], [4], [5], [6]. Danchev [3] introduced some necessary and sufficient conditions for all the normalized units are to be idempotent units for groups of orders 2 and 3. In this study, by considering some restrictions, we investigate necessary and sufficient conditions for equalities:i.V(R(G×H))=id(R(G×H)),ii.V(R(G×H))=G×id(RH),iii.V(R(G×H))=id(RG)×Hwhere G×H is the direct product of groups G and H. Therefore, the study can be seen as a generalization of [3], [4]. Notations mostly follow [12], [13].

Makale detayları

On Idempotent Units in Commutative Group Rings

Yazarlar: Ömer KÜSMÜŞ

Ana Başlıklar: Matematik

Dergi: Sakarya University Journal of Science 2020 Vol.24 Issue 4, pp.782-790

Belge Tipi: Makale

Yayın Tarihi: 7/2020

Belge Dili: İngilizce

Document ID (Org No.): 2000556787

DOI: https://doi.org/10.16984/saufenbilder.733935

Sayı

Yazarlar:

Ömer KÜSMÜŞ

Ana Başlıklar:

Matematik

Dergi:

Sakarya University Journal of Science 2020 Vol.24 Issue 4, pp.782-790

Belge Tipi:

Makale

Yayın Tarihi:

7/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000556787

DOI:

https://doi.org/10.16984/saufenbilder.733935