The annihilation graphs of commutator posets and lattices
Doctoral Thesis
2015
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University of Cape Town
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Abstract
We propose a new, widely generalized context for the study of the zero-divisor/ annihilating-ideal graphs, where the vertices of graphs are not elements/ideals of a commutative ring, but elements of an abstract ordered set (imitating the lattice of ideals), equipped with a binary operation (imitating products of ideals). The intermediate level of congruences of any algebraic structure admitting a "good" theory of commutators is also considered.
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Mehdinezhad, E. 2015. The annihilation graphs of commutator posets and lattices. University of Cape Town.