Annihilator graphs of MV-algebras

Aiping Gan; Yichuan Yang

doi:10.1142/S0219498821501887

Annihilator graphs of MV-algebras

Aiping Gan
, Yichuan Yang^*

^*Corresponding author for this work

School of Mathematical Sciences

Jiangxi Normal University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper, we introduce the annihilator graph AG(A) of an MV-algebra A. We show that AG(A) contains the zero-divisor graph ZG(A) as a spanning subgraph. We then prove that AG(A) = ZG(A) if and only if |A|≤ 4. Moreover, we obtain that the girth gr(AG(A)) {3, 4,∞}.

Original language	English
Article number	2150188
Journal	Journal of Algebra and its Applications
Volume	20
Issue number	10
DOIs	https://doi.org/10.1142/S0219498821501887
State	Published - 1 Oct 2021

Keywords

Annihilator graphs
MV-algebras
MV-semirings
Zero-divisor graphs

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10.1142/S0219498821501887

Cite this

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abstract = "In this paper, we introduce the annihilator graph AG(A) of an MV-algebra A. We show that AG(A) contains the zero-divisor graph ZG(A) as a spanning subgraph. We then prove that AG(A) = ZG(A) if and only if |A|≤ 4. Moreover, we obtain that the girth gr(AG(A)) \{3, 4,∞\}.",

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AB - In this paper, we introduce the annihilator graph AG(A) of an MV-algebra A. We show that AG(A) contains the zero-divisor graph ZG(A) as a spanning subgraph. We then prove that AG(A) = ZG(A) if and only if |A|≤ 4. Moreover, we obtain that the girth gr(AG(A)) {3, 4,∞}.

KW - Annihilator graphs

KW - MV-algebras

KW - MV-semirings

KW - Zero-divisor graphs

UR - https://www.scopus.com/pages/publications/85092243499

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DO - 10.1142/S0219498821501887

M3 - 文章

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VL - 20

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JF - Journal of Algebra and its Applications

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M1 - 2150188

ER -

Annihilator graphs of MV-algebras

Abstract

Keywords

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