Left-star order structure of Rickart *-rings
Insa Krēmere · Linear and Multilinear Algebra · 2015
Janowitz proved in 1983 that the initial segments of a Rickart *-ring with the star order are orthomodular posets. In this paper, the same result is proved for the left-star order , which was introduced by Marovtet al., by finding an orthogonality which corresponds to in a certain way and then applying a result proved by Cīrulis which states that the initial segments of any quasi-orthomodular set are orthomodular.