Partial orders on the power sets of Baer rings


Ungor B., Halicioglu S., Harmanci A., Marovt J.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.19, sa.1, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Konu: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1142/s0219498820500115
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Özet

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.