Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 60: Issue 2-3
Integral Closure of Powers of Generalized Edge Ideals
Author:
Sirajul Haque Ramakrishna Mission Vivekananda Educational and Research Institute, Belur, West Bengal, India

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Pages:
159–174
Online Publication Date:
24 Oct 2023
Publication Date:
24 Oct 2023
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2023.01543
Keywords:
Integral closure of ideal; generalized edge ideal; normal ideal
Restricted access

This article studies a new class of monomial ideals associated with a simple graph 𝐺, called generalized edge ideal, denoted by 𝐼𝑔(𝐺). Assuming that all the vertices 𝑥 have an exponent greater than 1 in 𝐼𝑔(𝐺), we completely characterize the graph 𝐺 for which 𝐼𝑔(𝐺) is integrally closed, and show that this is equivalent to 𝐼𝑔(𝐺) being normal i.e., all integral powers of 𝐼𝑔(𝐺) are integrally clased. We also give a necessary and sufficient condition for IgG=IgG¯ when 𝐺 is the star-shaped graph. Finally, we give a necessary and sufficient condition when the generalized edge ideal of a complete graph is integrally closed.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

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Studia Scientiarum Mathematicarum Hungarica
Language English
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Foundation		 1966
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ISSN 0081-6906 (Print)
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