The classification of rings with its genus of class of graphs

Thangaraj ASIR; Karuppiah MANO

Makale detayları

The classification of rings with its genus of class of graphs

Yazarlar:

Thangaraj ASIR | Karuppiah MANO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 3, pp.1424-1435

Belge Tipi:

Makale

Yayın Tarihi:

5/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745895

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

Let RRR be a commutative ring, III be a proper ideal of RRR, and S(I)={a∈R:ra∈I for some r∈R\smI}S(I)={a∈R:ra∈I for some r∈R\smI}S(I)=\{a\in R : ra\in I \text{ for some } r\in R\sm I\} be the set of all elements of RRR that are not prime to III. The total graph of RRR with respect to III, denoted by T(ΓI(R))T(ΓI(R))T(\Gamma_I(R)),  is the simple graph with all elements of RRR as vertices, and for distinct x,y∈Rx,y∈Rx,y\in R, the vertices xxx and yyy are adjacent if and only if x+y∈S(I)x+y∈S(I)x+y\in S(I). In this paper, we determine all isomorphic classes of commutative Artinian rings whose ideal-based total graph has genus at most two.

Makale detayları

The classification of rings with its genus of class of graphs

Yazarlar: Thangaraj ASIR | Karuppiah MANO

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2018 Vol.42 Issue 3, pp.1424-1435

Belge Tipi: Makale

Yayın Tarihi: 5/2018

Belge Dili: Türkçe

Document ID (Org No.): 2000745895

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Thangaraj ASIR | Karuppiah MANO

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2018 Vol.42 Issue 3, pp.1424-1435

Belge Tipi:

Makale

Yayın Tarihi:

5/2018

Belge Dili:

Türkçe

Document ID (Org No.):

2000745895

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098