Abstract
Abstract Considering prime Leavitt path algebras L K ( E ) {L_{K}(E)} , with E being an arbitrary graph with at least two vertices, and K being any field, we construct a class of maximal commutative subalgebras of L K ( E ) {L_{K}(E)} such that, for every algebra A from this class, A has zero intersection with the commutative core ℳ K ( E ) {\mathcal{M}_{K}(E)} of L K ( E ) {L_{K}(E)} defined and studied in [C. Gil Canto and A. Nasr-Isfahani, The commutative core of a Leavitt path algebra, J. Algebra 511 2018, 227–248]. We also give a new proof of the maximality, as a commutative subalgebra, of the commutative core ℳ R ( E ) {\mathcal{M}_{R}(E)} of an arbitrary Leavitt path algebra L R ( E ) {L_{R}(E)} , where E is an arbitrary graph and R is a commutative unital ring.
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