Abstract
ABSTRACTThe Bourque–Ligh conjecture states that if is a gcd-closed set of positive integers with distinct elements, then the LCM matrix is invertible. It is known that this conjecture holds for but does not generally hold for . In this paper, we study the invertibility of matrices in a more general matrix class, join matrices. At the same time, we provide a lattice-theoretic explanation for this solution of the Bourque–Ligh conjecture. In fact, let be a lattice, let be a subset of P and let be a function. We study under which conditions the join matrix on S with respect to f is invertible on a meet closed set S (i.e. .
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