A partial order on subsets of Baer bimodules with applications to C*-modules
Journal Of Algebra And Its Applications, cilt.11, sa.20, ss.21501951-215019519, 2021 (SCI-Expanded, Scopus)
- 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.