  An atomic monoid $M$ is called length-factorial if for every non-invertible
element $x \in M$, no two distinct factorizations of $x$ into irreducibles have
the same length (i.e., number of irreducible factors, counting repetitions).
The notion of length-factoriality was introduced by J. Coykendall and W. Smith
in 2011 under the term 'other-half-factoriality': they used length-factoriality
to provide a characterization of unique factorization domains. In this paper,
we study length-factoriality in the more general context of commutative,
cancellative monoids. In addition, we study factorization properties related to
length-factoriality, namely, the PLS property (recently introduced by Chapman
et al.) and bi-length-factoriality in the context of semirings.
