On the connectedness of \(f\)-simplicial complexes. (English) Zbl 1362.13029

The authors in this paper introduce the notion of a \(f\)-simplicial complex which generalises the term \(f\)-graph defined in [G. Q. Abbasi et al., Algebra Colloq. 19, 921–926 (2012; Zbl 1294.13031)]. They mainly interested in studying the connectedness and disconnectedness property. They show that a pure \(f\)-simplicial complex of dimension \(\geq 2\) is connected. In their next result, they give a complete characterisation of disconnected \(f\)-graphs.


13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)
13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes
13C14 Cohen-Macaulay modules


Zbl 1294.13031
Full Text: DOI


[1] Abbasi, G. Q.; Ahmad, S.; Anwar, I.; Baig, W. A., \(f\)-ideals of degree \(2\), Algebra Colloq., 19, Spec 1, 921-926, (2012) · Zbl 1294.13031
[2] Anwar, I.; Mahmood, H.; Binyamin, M. A.; Zafar, M. K., On the characterization of \(f\)-ideals, Commun. Algebra, 42, 9, 3736-3741, (2014) · Zbl 1328.13029
[3] Bruns, W.; Herzog, J., Cohen-Macaulay Rings, 39, (1998), Cambrigde University Press
[4] Buchstaber, V. M.; Panov, T. E., Toric Topology, Mathematical Surveys and Monographs, 204, (2015), American Mathematical Society, Providence, RI
[5] Faridi, S., The facet ideal of a simplicial complex, Manuscripta Math., 109, 159-174, (2002) · Zbl 1005.13006
[6] Guo, J.; Wu, T., On the \((n, d)\)th \(f\)-ideals, J. Korean Math. Soc., 52, 4, 685-697, (2015) · Zbl 1327.13100
[7] J. Guo, T. Wu and Q. Liu, Perfect sets and \(f\)-ideals, preprint (2013), arXiv:1312.0324 [math.AC].
[8] Herzog, J.; Hibi, T., Monomial Algebra, (2009), Springer-Verlag, New York
[9] Mahmood, H.; Anwar, I.; Zafar, M. K., Construction of Cohen-macauly \(f\)-graphs, J. Algebra Appl., 13, 6, 14500121, (2014)
[10] Villarreal, R. H., Monomial Algebras, (2001), Dekker, New York
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