Öz
Kaynakça
- [1] P. Danchev, “Trivial units in commutative group algebras,” Extr. Math., vol. 23, pp. 49-60, 2008.
- [2] P. Danchev, “Trivial units in abelian group algebras,” Extr. Math., vol. 24, pp. 47-53, 2009.
- [3] P. Danchev, “Idempotent units in commutative group rings,” Kochi J. Math, vol. 4, pp. 61-68, 2009.
- [4] P. Danchev, “Idempotent units of commutative group rings,” Commun. Algebra, vol. 38, pp. 4649-4654, 2010.
- [5] P. Danchev, “On some idempotent torsion decompositions of normed units in commutative group rings,” J. Calcutta Math. Soc., vol. 6, pp. 31-34, 2010.
- [6] P. Danchev, “Idempotent-torsion normalized units in abelian group rings,” Bull Calcutta Math. Soc., to appear, 2011.
- [7] G. Karpilovsky, “On units in commutative group rings,” Arch. Math. (Basel), vol. 38, pp. 420–422, 1982.
- [8] G. Karpilovsky, “On finite generation of unit groups of commutative group rings,” Arch. Math. (Basel), vol. 40, pp. 503–508, 1983.
- [9] G. Karpilovsky, “Unit groups of group rings,” Harlow: Longman Sci. and Techn., 1989.
- [10] G. Karpilovsky, “Units of commutative group algebras,” Expo. Math., vol. 8, pp. 247-287, 1990.
- [11] W. May, “Group algebras over finitely generated rings,” J. Algebra vol. 39 pp. 483–511, 1976.
- [12] C. Polcino Milies and S. K. Sehgal, “An introduction to group rings,” Kluwer, North-Holland, Amsterdam, 2002.
- [13] S. K. Sehgal, “Topics in group rings,” Marcel Dekker, New York, 1978.
Öz
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].
Anahtar Kelimeler
Kaynakça
- [1] P. Danchev, “Trivial units in commutative group algebras,” Extr. Math., vol. 23, pp. 49-60, 2008.
- [2] P. Danchev, “Trivial units in abelian group algebras,” Extr. Math., vol. 24, pp. 47-53, 2009.
- [3] P. Danchev, “Idempotent units in commutative group rings,” Kochi J. Math, vol. 4, pp. 61-68, 2009.
- [4] P. Danchev, “Idempotent units of commutative group rings,” Commun. Algebra, vol. 38, pp. 4649-4654, 2010.
- [5] P. Danchev, “On some idempotent torsion decompositions of normed units in commutative group rings,” J. Calcutta Math. Soc., vol. 6, pp. 31-34, 2010.
- [6] P. Danchev, “Idempotent-torsion normalized units in abelian group rings,” Bull Calcutta Math. Soc., to appear, 2011.
- [7] G. Karpilovsky, “On units in commutative group rings,” Arch. Math. (Basel), vol. 38, pp. 420–422, 1982.
- [8] G. Karpilovsky, “On finite generation of unit groups of commutative group rings,” Arch. Math. (Basel), vol. 40, pp. 503–508, 1983.
- [9] G. Karpilovsky, “Unit groups of group rings,” Harlow: Longman Sci. and Techn., 1989.
- [10] G. Karpilovsky, “Units of commutative group algebras,” Expo. Math., vol. 8, pp. 247-287, 1990.
- [11] W. May, “Group algebras over finitely generated rings,” J. Algebra vol. 39 pp. 483–511, 1976.
- [12] C. Polcino Milies and S. K. Sehgal, “An introduction to group rings,” Kluwer, North-Holland, Amsterdam, 2002.
- [13] S. K. Sehgal, “Topics in group rings,” Marcel Dekker, New York, 1978.
Ayrıntılar
| 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 |
Kaynak Göster
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INDEXING & ABSTRACTING & ARCHIVING
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