期刊名称：AKCE International Journal of Graphs and Combinatorics
印刷版ISSN：0972-8600
出版年度：2019
卷号：16
期号：1
页码：57-65
DOI：10.1016/j.akcej.2018.04.001
语种：English
出版社：Elsevier
摘要：AbstractIn this paper, we introduce a partial order on rings with involution, which is a generalization of the partial order on the set of projections in a Rickart∗-ring. We prove that a∗-ring with the natural partial order forms a sectionally semi-complemented poset. It is proved that every interval[0,x]forms a Boolean algebra in case of abelian Rickart∗-rings. The concepts of generalized comparability(GC)and partial comparability(PC)are extended to involve all the elements of a∗-ring. Further, it is proved that these concepts are equivalent in finite abelian Rickart∗-rings.
