dc.contributor.author | Anderson, David F. | |
dc.contributor.author | Badawi, Ayman | |
dc.date.accessioned | 2022-11-28T11:33:15Z | |
dc.date.available | 2022-11-28T11:33:15Z | |
dc.date.issued | 2022-04-16 | |
dc.identifier.citation | Anderson, D. F., & Badawi, A. (2022). The n-zero-divisor graph of a commutative semigroup. In Communications in Algebra (Vol. 50, Issue 10, pp. 4155–4177). Informa UK Limited. https://doi.org/10.1080/00927872.2022.2057521 | en_US |
dc.identifier.issn | 1532-4125 | |
dc.identifier.uri | http://hdl.handle.net/11073/25070 | |
dc.description.abstract | Let S be a (multiplicative) commutative semigroup with 0, Z(S) the set of zero-divisors of S, and n a positive integer. The zero-divisor graph of S is the (simple) graph Γ(S) with vertices Z(S) ∗ = Z(S) \ {0}, and distinct vertices x and y are adjacent if and only if xy = 0. In this paper, we introduce and study the n-zero-divisor graph of S as the (simple) graph Γn(S) with vertices Zn(S) ∗ = {x n | x ∈ Z(S)} \ {0}, and distinct vertices x and y are adjacent if and only if xy = 0. Thus each Γn(S) is an induced subgraph of Γ(S) = Γ1(S). We pay particular attention to diam(Γn(S)), gr(Γn(S)), and the case when S is a commutative ring with 1 6= 0. We also consider several other types of “n-zero-divisor” graphs and commutative rings such that some power of every element (or zero-divisor) is idempotent. | en_US |
dc.language.iso | en_US | en_US |
dc.publisher | Taylor and Francis | en_US |
dc.relation.uri | https://doi.org/10.1080/00927872.2022.2057521 | en_US |
dc.subject | Idempotent elements | en_US |
dc.subject | Zero-divisors | en_US |
dc.subject | Commutative semigroup with zero | en_US |
dc.subject | Commutative ring with identity | en_US |
dc.subject | Von Neumann regular ring | en_US |
dc.subject | π-regular ring | en_US |
dc.subject | Zero-divisor graph | en_US |
dc.subject | Annihilator graph | en_US |
dc.subject | Extended zero-divisor graph | en_US |
dc.subject | Congruence-based zero-divisor graph | en_US |
dc.title | The n-zero-divisor graph of a commutative semigroup | en_US |
dc.type | Article | en_US |
dc.type | Peer-Reviewed | en_US |
dc.type | Postprint | en_US |
dc.identifier.doi | 10.1080/00927872.2022.2057521 | |