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Research Articles

On the strong persistence property and normality of cover ideals of theta graphs

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Pages 3782-3791 | Received 31 Aug 2020, Accepted 01 Mar 2023, Published online: 20 Mar 2023

References

  • Al-Ayyoub, I., Nasernejad, M., Roberts, L. (2019). Normality of cover ideals of graphs and normality under some operations. Results Math. 74(4):26. DOI:10.1007/s00025-019-1068-x.
  • Bondy, J. A., Murty, U. S. R. (2008). Graph Theory. Graduate Texts in Mathematics, 244. New York: Springer, xii+651 pp.
  • Brodmann, M. (1979). Asymptotic stability of Ass(M/InM). Proc. Amer. Math. Soc. 74:16–18.
  • Escobar, C., Villarreal, R. H., Yoshino, Y. (2006). Torsion-freeness and normality of blowup rings of monomial ideals. In: Corso, A., Gimenez, P., Pinto, M. V., Zarzuela, S., eds. Commutative Algebra. Lecture Notes in Pure and Applied Mathematics, Vol. 244. Boca Raton, FL: Chapman & Hall/CRC, pp. 69–84.
  • Faridi, S. (2005). Monomial ideals via square-free monomial ideals. In: Corso, A., Gimenez, P., Pinto, M. V., Zarzuela, S., eds. Commutative Algebra. Lecture Notes in Pure and Applied Mathematics, Vol. 244. Boca Raton, FL: Chapman & Hall/CRC, pp. 85–114.
  • Francisco, C., Hà, H. T., Van Tuyl, A. (2011). Colorings of hypergraphs, perfect graphs and associated primes of powers of monomial ideals. J. Algebra 331:224–242.
  • Gitler, I., Reyes, E., Villarreal, R. H. (2005). Blowup algebras of ideals of vertex covers of bipartite graphs. Contemp. Math. 376:273–279.
  • Grayson, D. R., Stillman, M. E. Macaulay2, a software system for research in algebraic geometry. http://www.math.uiuc.edu/Macaulay2/.
  • Herzog, J., Hibi, T. (2011). Monomial Ideals. Graduate Texts in Mathematics, Vol. 260. London: Springer-Verlag.
  • Herzog, J., Qureshi, A. A. (2015). Persistence and stability properties of powers of ideals. J. Pure Appl. Algebra 219:530–542.
  • Kaiser, T., Stehlík, M., Škrekovski, R. (2014). Replication in critical graphs and the persistence of monomial ideals. J. Comb. Theory, Ser. A 123:239–251.
  • Khashyarmanesh, K., Nasernejad, M. (2014). On the stable set of associated prime ideals of monomial ideals and square-free monomial ideals. Commun. Algebra 42:3753–3759.
  • Khashyarmanesh, K., Nasernejad, M., Toledo, J. (2021). Symbolic strong persistence property under monomial operations and strong persistence property of cover ideals. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 64(112):103–129.
  • Martinez-Bernal, J., Morey, S., Villarreal, R. H. (2012). Associated primes of powers of edge ideals. Collect. Math. 63:361–374.
  • Matsumura, H. (1986). Commutative Ring Theory. Cambridge: Cambridge University Press.
  • Mohammadi, F., Kiani, D. (2010). Sequentially Cohen-Macaulay graphs of form θn1,…,nk. Bull. Iran. Math. Soc. 36(2):109–118.
  • Nasernejad, M. (2017). Persistence property for some classes of monomial ideals in a polynomial ring. J. Algebra Appl. 16:1750105 (17 pages).
  • Nasernejad, M., Khashyarmanesh, K. (2017). On the Alexander dual of the path ideals of rooted and unrooted trees. Commun. Algebra 45:1853–1864.
  • Nasernejad, M., Khashyarmanesh, K., Al-Ayyoub, I. (2019). Associated primes of powers of cover ideals under graph operations. Commun. Algebra 47(5):1985–1996.
  • Nasernejad, M., Qureshi, A. A., Bandari, S., Musapaşaoğlu, A. (2022). Dominating ideals and closed neighborhood ideals of graphs. Mediterr. J. Math. 19(4):Paper No. 152, 18 pp.
  • Rajaee, S., Nasernejad, M., Al-Ayyoub, I. (2018). Superficial ideals for monomial ideals. J. Algebra Appl. 16(2):1850102 28pp.
  • Ratliff, Jr., L. J. (1976). On prime divisors of In, n large. Michigan Math. J. 23:337–352.
  • Restuccia, G., Villarreal, R. H. (2001). On the normality of monomial ideals of mixed products. Commun. Algebra 29:3571–3580.
  • Reyes, E., Toledo, J. (2017). On the strong persistence property for monomial ideals. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 60(108):293–305.
  • Simis, A., Vasconcelos, W., Villarreal, R. (1994). On the ideal theory of graphs. J. Algebra 167:389–416.
  • Villarreal, R. H. (2015). Monomial Algebras. Monographs and Research Notes in Mathematics, 2nd ed. Boca Raton, FL: CRC Press.
  • Villarreal, R. H. (1996). Normality of subrings generated by square-free monomials. J. Pure Appl. Algebra 113:91–106.
  • Villarreal, R. H. (2008). Rees cones and monomial rings of matroids. Linear Algebra Appl. 428:2933–2940.

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