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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.

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

Citations:

Zbl 1294.13031
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References:

[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
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