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Marovt, Janko; Rakić, Dragan S.; Djordjević, Dragan S.
Linear & multilinear algebra, 02/2015, Letnik: 63, Številka: 2Journal Article
Let be a unital ring admitting involution. We introduce an order on and show that in the case when is a Rickart -ring, this order is equivalent to the well-known star partial order. The notion of the left-star and the right-star partial orders is extended to Rickart -rings. Properties of the star, the left-star and the right-star partial orders are studied in Rickart -rings and some known results are generalized. We found matrix forms of elements and when , where is one of these orders. Conditions under which these orders are equivalent to the minus partial order are obtained. The diamond partial order is also investigated.
