  We formulate a type B extended nilHecke algebra, following the type A
construction of Naisse and Vaz. We describe an action of this algebra on
extended polynomials and describe some results on the structure on the extended
symmetric polynomials. Finally, following Appel, Egilmez, Hogancamp, and Lauda,
we prove a result analogous to a classical theorem of Solomon connecting the
extended symmetric polynomial ring to a ring of usual symmetric polynomials and
their differentials.
