A partial order on subsets of Baer bimodules with applications to C*-modules

Birkenmeier G., Kara Şen Y.

Journal Of Algebra And Its Applications, cilt.11, sa.20, ss.21501951-215019519, 2021 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 20
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1142/s0219498821501954
  • 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
  • Sayfa Sayıları: ss.21501951-215019519
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

In this paper, we introduce the concept of Baer (p, q)-sets. Using this notion, we define

Rickart, Baer, quasi-Baer and π-Baer (S,R)-bimodules, respectively. We show how these

conditions relate to each other. We also develop new properties of the minus binary

relation, ≤-, we extend the relation ≤- to (S,R)-bimodules and use it to characterize

the aforementioned Rickart, Baer, quasi-Baer, and π-Baer (S,R)-bimodules. Moreover,

we specify subsets K of the power set of a (S,R)-bimodule for which ≤- determines a

partial order and for which ≤- is a lattice. We analyze the relation ≤- by examining the

associated Baer (p, q)-sets. Finally, we apply our results to C∗-modules. Examples are

provided to illustrate and delimit our results.