Identities over the two-element alphabet

In 4] and 5] the authors considered semigroup identities that induce various types of decompositions. In this paper we continue this work for identites over the two-element alphabet. In particular, we solve some problems that are not solved in the general case and we solve several types of well known Tamura's problems. Supported by Grant 0401A of RFNS through Math. Inst. SANU.