Published January 1, 2020 | Version v1
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Partial orders on the power sets of Baer rings

  • 1. Ankara Univ, Dept Math, TR-06100 Ankara, Turkey
  • 2. Hacettepe Univ, Dept Math, TR-06800 Ankara, Turkey
  • 3. Univ Maribor, Fac Econ & Business, Razlagova 14, SI-2000 Maribor, Slovenia

Description

Let R be a ring. Motivated by a generalization of a well-known minus partial order to Rickart rings, we introduce a new relation on the power set P(R) of R and show that this relation, which we call "the minus order on P(R)", is a partial order when R is a Baer ring. We similarly introduce and study properties of the star, the left-star, and the right-star partial orders on the power sets of Baer *-rings. We show that some ideals generated by projections of a von Neumann regular and Baer *-ring R. form a lattice with respect to the star partial order on P(R). As a particular case, we present characterizations of these orders on the power set of B(H), the algebra of all bounded linear operators on a Hilbert space H.

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