A lemma stated without proof by Y. Komori 

in a paper on a class of algebras related to 

$BCK$-algebras (to show that this class is 

not a variety) is here given a proof 

and applied to a broader class of algebras, 

which we call Komori algebras. The idea Komori 

had in mind for a proof can be gathered 

from a paper by M. Nagayama in which the lemma 

is proved for the class of $BCK$-algebras and 

used to show that this class is not a variety. 

The Komori algebras of the  present note are 

defined by abstracting away everything not 

essential to this proof. This permits 

a formulation of the Lemma 

in the following general form: a non-trivial 

quasivariety of Komori algebras is a variety 

only if it satisfies some non-degenerate 

alien identity. Here an alien identity is 

one in which the rightmost variables of 

the two terms involves are distinct, 

and such an identity is non-degenerate 

if neither of these terms is equal to 1 

(a constant in Komori algebras) 

over the quasivariety concerned.