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)×H
where 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].
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Yayımlanma Tarihi | 1 Ağustos 2020 |
Gönderilme Tarihi | 7 Mayıs 2020 |
Kabul Tarihi | 10 Haziran 2020 |
Yayımlandığı Sayı | Yıl 2020 Cilt: 24 Sayı: 4 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.