Not each sequential effect algebra is sharply dominating

Let E   be an effect algebra and EsEs be the set of all sharp elements of E. E   is said to be sharply dominating if for each a∈Ea∈E there exists a smallest element aˆ∈Es such that a⩽aˆ. In 2002, Professors Gudder and Greechie proved that each σ-sequential effect algebra is sharply dominating. In 2005, Professor Gudder presented 25 open problems in [S. Gudder, Int. J. Theory Phys. 44 (2005) 2219], the 3rd problem asked: Is each sequential effect algebra sharply dominating? Now, we construct an example to answer the problem negatively.