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- W4254151905 abstract "As an extension of [Formula: see text] (the annihilation graph of the commutator poset (lattice) [Formula: see text] with respect to an element [Formula: see text]), we discuss when [Formula: see text] (the annihilation graph of the commutator poset (lattice) [Formula: see text] with respect to an ideal [Formula: see text]) is a complete bipartite ([Formula: see text]-partite) graph together with some of its other graph-theoretic properties. We investigate the interplay between some (order-) lattice-theoretic properties of [Formula: see text] and graph-theoretic properties of its associated graph [Formula: see text]. We provide some examples to show that some conditions are not superfluous assumptions. We prove and show by a counterexample that the class of lower sets of a commutator poset [Formula: see text] is properly contained in the class of [Formula: see text]-ideals of [Formula: see text] (i.e. multiplicatively absorptive ideals (sets) of [Formula: see text] that are defined by commutator operation)." @default.
- W4254151905 created "2022-05-12" @default.
- W4254151905 creator A5023082714 @default.
- W4254151905 creator A5081493407 @default.
- W4254151905 date "2018-05-23" @default.
- W4254151905 modified "2023-09-27" @default.
- W4254151905 title "The annihilation graphs of commutator posets and lattices with respect to an ideal" @default.
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- W4254151905 doi "https://doi.org/10.1142/s0219498818501037" @default.
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