Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2017, , 115 - 122, 09.01.2017
https://doi.org/10.13069/jacodesmath.284939

Öz

Kaynakça

  • [1] V. Camillo, W. K. Nicholson, On rings where left principal ideals are left principal annihilator, Int. Electron. J. Algebra 17 (2015) 199–214.
  • [2] T. J. Dorsey, Morphic and principal–ideal group rings, J. Algebra 318(1) (2007) 393–411.
  • [3] J. L. Fisher, S. K. Sehgal, Principal ideal group rings, Comm. Algebra 4(4) (1976) 319–325.
  • [4] P. Hurley, T. Hurley, Module codes in group rings, Proc. Int. Symp. Information Theory (ISIT) (2007) 1981–1985.
  • [5] P. Hurley, T. Hurley, Codes from zero–divisors and units in group rings, Int. J. Inf. Coding Theory (2009) 57–87.
  • [6] S. Jitman, S. Ling, H. Liu, X. Xie, Checkable codes from group rings, arXiv:1012.5498, 2010.
  • [7] F. J. MacWilliams, Codes and ideals in group algebras, Combinatorial Mathematics and its Applications (1969) 317–328.
  • [8] W. K. Nicholson, E. Sánchez Campos, Rings with the dual of the isomorphism theorem, J. Algebra 271(1) (2004) 391–406.

Code–checkable group rings

Yıl 2017, , 115 - 122, 09.01.2017
https://doi.org/10.13069/jacodesmath.284939

Öz

A code over a group ring is defined to be a submodule of that group ring. For a code $C$ over a group ring $RG$, $C$ is said to be checkable if there is $v\in RG$ such that {$C=\{x\in RG: xv=0\}$}. In \cite{r2}, Jitman et al. introduced the notion of code-checkable group ring. We say that a group ring $RG$ is code-checkable if every ideal in $RG$ is a checkable code. In their paper, Jitman et al. gave a necessary and sufficient condition for the group ring $\mathbb{F}G$, when $\mathbb{F}$ is a finite field and $G$ is a finite abelian group, to be code-checkable. In this paper, we give some characterizations for code-checkable group rings for more general alphabet. For instance, a finite commutative group ring $RG$, with $R$ is semisimple, is code-checkable if and only if $G$ is $\pi'$-by-cyclic $\pi$; where $\pi$ is the set of noninvertible primes in $R$. Also, under suitable conditions, $RG$ turns out to be code-checkable if and only if it is pseudo-morphic.

Kaynakça

  • [1] V. Camillo, W. K. Nicholson, On rings where left principal ideals are left principal annihilator, Int. Electron. J. Algebra 17 (2015) 199–214.
  • [2] T. J. Dorsey, Morphic and principal–ideal group rings, J. Algebra 318(1) (2007) 393–411.
  • [3] J. L. Fisher, S. K. Sehgal, Principal ideal group rings, Comm. Algebra 4(4) (1976) 319–325.
  • [4] P. Hurley, T. Hurley, Module codes in group rings, Proc. Int. Symp. Information Theory (ISIT) (2007) 1981–1985.
  • [5] P. Hurley, T. Hurley, Codes from zero–divisors and units in group rings, Int. J. Inf. Coding Theory (2009) 57–87.
  • [6] S. Jitman, S. Ling, H. Liu, X. Xie, Checkable codes from group rings, arXiv:1012.5498, 2010.
  • [7] F. J. MacWilliams, Codes and ideals in group algebras, Combinatorial Mathematics and its Applications (1969) 317–328.
  • [8] W. K. Nicholson, E. Sánchez Campos, Rings with the dual of the isomorphism theorem, J. Algebra 271(1) (2004) 391–406.
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

Noha Abdelghany Bu kişi benim

Nefertiti Megahed Bu kişi benim

Yayımlanma Tarihi 9 Ocak 2017
Yayımlandığı Sayı Yıl 2017

Kaynak Göster

APA Abdelghany, N., & Megahed, N. (2017). Code–checkable group rings. Journal of Algebra Combinatorics Discrete Structures and Applications, 4(2 (Special Issue: Noncommutative rings and their applications), 115-122. https://doi.org/10.13069/jacodesmath.284939
AMA Abdelghany N, Megahed N. Code–checkable group rings. Journal of Algebra Combinatorics Discrete Structures and Applications. Mayıs 2017;4(2 (Special Issue: Noncommutative rings and their applications):115-122. doi:10.13069/jacodesmath.284939
Chicago Abdelghany, Noha, ve Nefertiti Megahed. “Code–checkable Group Rings”. Journal of Algebra Combinatorics Discrete Structures and Applications 4, sy. 2 (Special Issue: Noncommutative rings and their applications) (Mayıs 2017): 115-22. https://doi.org/10.13069/jacodesmath.284939.
EndNote Abdelghany N, Megahed N (01 Mayıs 2017) Code–checkable group rings. Journal of Algebra Combinatorics Discrete Structures and Applications 4 2 (Special Issue: Noncommutative rings and their applications) 115–122.
IEEE N. Abdelghany ve N. Megahed, “Code–checkable group rings”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy. 2 (Special Issue: Noncommutative rings and their applications), ss. 115–122, 2017, doi: 10.13069/jacodesmath.284939.
ISNAD Abdelghany, Noha - Megahed, Nefertiti. “Code–checkable Group Rings”. Journal of Algebra Combinatorics Discrete Structures and Applications 4/2 (Special Issue: Noncommutative rings and their applications) (Mayıs 2017), 115-122. https://doi.org/10.13069/jacodesmath.284939.
JAMA Abdelghany N, Megahed N. Code–checkable group rings. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4:115–122.
MLA Abdelghany, Noha ve Nefertiti Megahed. “Code–checkable Group Rings”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy. 2 (Special Issue: Noncommutative rings and their applications), 2017, ss. 115-22, doi:10.13069/jacodesmath.284939.
Vancouver Abdelghany N, Megahed N. Code–checkable group rings. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4(2 (Special Issue: Noncommutative rings and their applications):115-22.