The Logic Order on a Generalized Hermitian Algebra

In this paper, a new order, the so-called logic order, is introduced on a generalized Hermitian algebra. We investigate the existence of the infima and the suprema of elements with respect to the logic order in the generalized Hermitian algebra, and give an explicit expression for the infimum of e and p, where p is a projection and e belongs to the unit interval involving the original ordering. Moreover, we also obtain that in regard to this new order, a generalized Hermitian algebra forms a generalized orthomodular poset.