The Specht property of $L$-varieties of vector spaces over an arbitrary field

We study the Specht property for $L$-varieties of vector spaces embedded in associative algebras over an arbitrary field. An $L$-variety with no finite basis of identities over a field, which is the join of two Spechtian $L$-varieties, is exemplified. A condition under which $L$-varieties will have the Specht property is found.