Partial orders on the power sets of Baer rings

ÜNGÖR B., HALICIOĞLU S., Harmanci A., Marovt J.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.19, sa.1, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 1
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1142/s0219498820500115
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Minus partial order, star partial order, left-star partial order, right-star partial order, Baer ring, Baer *-ring, LEFT-STAR
  • Ankara Üniversitesi Adresli: Evet

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.