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In a recent paper we assigned to each positive variety V and a fixed natural number k the class of all (positive) boolean combinations of the restricted polynomials, i.e. the languages of the form L0a1L1a2 . . . a L , where ≤ k, a1, . . . , a are letters and L0, . . . , L are from the variety V. For this polynomial operator on a wide class of varieties we gave a certain algebraic counterpart which works with identities satisfied by syntactic (ordered) monoids of considered languages. Here wedoi:10.1142/s021819671100690x fatcat:hhu4fq4lzjeqholbzp7ziezuc4