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Mahmood, H.; Anwar, I.; Binyamin, M. A.; Yasmeen, S.

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

J. Algebra Appl. 16, No. 1, Article ID 1750017, 9 p. (2017).
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.
Reviewer: Clare D’Cruz (Kelambakkam)

Cited in 4 Documents

MSC:

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

Keywords:

connected simplicial complex; \(f\)-ideal; \(f\)-graph; facet ideal

Citations:

Zbl 1294.13031
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\textit{H. Mahmood} et al., J. Algebra Appl. 16, No. 1, Article ID 1750017, 9 p. (2017; Zbl 1362.13029)
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References:

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[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
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[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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