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On the genus of the kk-maximal hypergraph of commutative rings

    https://doi.org/10.1142/S1793830919500101Cited by:1 (Source: Crossref)

    Let RR be a commutative ring with identity and k2k2, a fixed integer. Let (R,k) be the set of all k-maximal elements in R. Associate a k-maximal hypergraphk(R) to R with vertex set (R,k) and for distinct elements a1,a2,,ak in (R,k), the set {a1,a2,,ak} is an edge of k(R) if and only if ki=1Rai=R and ki=1ijRaiR for all 1jk. In this paper, we determine all isomorphism classes of finite commutative non-local rings with identity whose k-maximal hypergraph has genus one. Finally, we classify all finite commutative non-local rings R for which 3(R) is projective.

    AMSC: 05C25, 05C75, 13A15, 13M05
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