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Nearly Normally Torsionfree Ideals

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Combinatorial Structures in Algebra and Geometry (NSA 2018)

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Abstract

We describe all connected graphs whose edge ideals are nearly normally torsionfree. We also prove that the facet ideal of a special odd cycle is nearly normally torsionfree. Finally, we give a necessary condition for a t-spread principal Borel ideal generated in degree 3 to be nearly normally torsionfree.

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References

  1. C. Andrei, V. Ene, B. Lajmiri, Powers of \(t\)-spread principal Borel ideals. Arch. Math. (Basel) 112(6), 587–597 (2019)

    Article  MathSciNet  Google Scholar 

  2. M. Brodmann, Asymptotic stability of \({\rm Ass}(M/I^{n}M)\). Proc. Am. Math. Soc. 74(1), 16–18 (1979)

    MathSciNet  MATH  Google Scholar 

  3. J. Chen, S. Morey, A. Sung, The stable set of associated primes of the ideal of a graph. Rocky Mt. J. Math. 32(1), 71–89 (2002)

    Article  MathSciNet  Google Scholar 

  4. V. Ene, J. Herzog, A. Asloob Qureshi, \(t\)-spread strongly stable monomial ideals. Comm. Algebra 47(12), 5303–5316 (2019)

    Google Scholar 

  5. C.A. Francisco, H.T. Hà, A. Van Tuyl, Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals. J. Algebra 331, 224–242 (2011)

    Article  MathSciNet  Google Scholar 

  6. H.T. Hà, S. Morey, Embedded associated primes of powers of square-free monomial ideals. J. Pure Appl. Algebra 214(4), 301–308 (2010)

    Article  MathSciNet  Google Scholar 

  7. J. Herzog, T. Hibi, Monomial Ideals, vol. 260, Graduate Texts in Mathematics (Springer, London Ltd, London, 2011)

    Google Scholar 

  8. J. Herzog, T. Hibi, N.V. Trung, Symbolic powers of monomial ideals and vertex cover algebras. Adv. Math. 210(1), 304–322 (2007)

    Article  MathSciNet  Google Scholar 

  9. J. Herzog, B. Lajmiri, F. Rahmati, On the associated prime ideals and the depth of powers of squarefree principal Borel ideals. Int. Electron. J. Algebra 26, 224–244 (2019)

    Article  MathSciNet  Google Scholar 

  10. J. Herzog, A. Rauf, M. Vladoiu, The stable set of associated prime ideals of a polymatroidal ideal. J. Algebraic Combin. 37(2), 289–312 (2013)

    Article  MathSciNet  Google Scholar 

  11. B. Lajmiri, F. Rahmati, Properties of \(t\)-spread principal borel ideals generated in degree two. Facta Univ. 35(1), 131–140 (2019)

    MathSciNet  Google Scholar 

  12. J. Martínez-Bernal, S. Morey, R.H. Villarreal, Associated primes of powers of edge ideals. Collect. Math. 63(3), 361–374 (2012)

    Article  MathSciNet  Google Scholar 

  13. M. Nasernejad, K. Khashyarmanesh, I. Al-Ayyoub, Associated primes of powers of cover ideals under graph operations. Comm. Algebra 47(5), 1985–1996 (2019)

    Article  MathSciNet  Google Scholar 

  14. A. Simis, W.V. Vasconcelos, R.H. Villarreal, On the ideal theory of graphs. J. Algebra 167(2), 389–416 (1994)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

I would like to thank the anonymous referee for pointing out an error in the first version of the manuscript and for the valuable comments. I am also very grateful to Professor Viviana Ene for valuable suggestions and comments during the preparation of this paper. I gratefully acknowledge the financial support awarded by BITDEFENDER.

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Authors and Affiliations

  1. Simion Stoilow Institute of Mathematics of the Romanian Academy, Calea Grivitei 21, 010702, Bucharest, Romania

    Claudia Andrei-Ciobanu

Authors
  1. Claudia Andrei-Ciobanu
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Correspondence to Claudia Andrei-Ciobanu .

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Editors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest, Romania

    Dumitru I. Stamate

  2. Department of Mathematics, Pedagogical University of Cracow, Kraków, Poland

    Tomasz Szemberg

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Andrei-Ciobanu, C. (2020). Nearly Normally Torsionfree Ideals. In: Stamate, D., Szemberg, T. (eds) Combinatorial Structures in Algebra and Geometry. NSA 2018. Springer Proceedings in Mathematics & Statistics, vol 331. Springer, Cham. https://doi.org/10.1007/978-3-030-52111-0_1

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