On Somosʹ dissection identities

We give proofs of a list of M. Somosʹ dissection identities. An eta function identity presented by B.C. Berndt and W.B. Hart, a theorem by H.-C. Chan on the congruence property of a ( n ) with generating function ( q ; q ) ∞ − 1 ( q 2 ; q 2 ) ∞ − 1 , and a theorem by G.E. Andrews, A. Schilling, and S.O. Warnaar are shown to be related to dissection identities. Several new corollaries are also presented as applications.