On a graph of ideals of a commutative ring
| dc.contributor.author | Khoramdel, Mehdi | |
| dc.contributor.author | Atani, Shahabaddin Ebrahimi | |
| dc.contributor.author | Pishhesari, Saboura Dolati | |
| dc.contributor.department | Other | tr_TR |
| dc.contributor.faculty | Other | tr_TR |
| dc.date.accessioned | 2021-11-09T11:36:42Z | |
| dc.date.available | 2021-11-09T11:36:42Z | |
| dc.date.issued | 2019-08-01 | |
| dc.description.abstract | In this paper, we introduce and investigate a new graph of a commutative ring R, denoted by G(R), with all nontrivial ideals of R as vertices, and two distinct vertices I and J are adjacent if and only if ann(I∩J)=ann(I)+ann(J). In this article, the basic properties and possible structures of the graph G(R) are studied and investigated as diameter, girth, clique number, cut vertex and domination number. We characterize all rings R for which G(R) is planar, complete and complete r-partite. We show that, if (R,M) is a local Artinian ring, then G(R) is complete if and only if Soc(R) is simple. Also, it is shown that if R is a ring with G(R) is r-regular, then either G(R) is complete or null graph. Moreover, we show that if R is an Artinian ring, then R is a serial ring if and only if G(R/I) is complete for each ideal I of R. | tr_TR |
| dc.description.index | Trdizin | tr_TR |
| dc.identifier.endpage | 2297 | tr_TR |
| dc.identifier.issn/e-issn | 2618-6470 | |
| dc.identifier.issue | 2 | tr_TR |
| dc.identifier.startpage | 2283 | tr_TR |
| dc.identifier.uri | https://doi.org/10.31801/cfsuasmas.534944 | tr_TR |
| dc.identifier.uri | http://hdl.handle.net/20.500.12575/75962 | |
| dc.identifier.volume | 68 | tr_TR |
| dc.language.iso | en | tr_TR |
| dc.publisher | Ankara Üniversitesi Fen Fakültesi | tr_TR |
| dc.relation.isversionof | 10.31801/cfsuasmas.534944 | tr_TR |
| dc.relation.journal | Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics | tr_TR |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Başka Kurum Yazarı | tr_TR |
| dc.subject | Ideals | tr_TR |
| dc.subject | Clique number | tr_TR |
| dc.subject | Complete r-partite | tr_TR |
| dc.title | On a graph of ideals of a commutative ring | tr_TR |
| dc.type | Article | tr_TR |