A partial order on subsets of Baer bimodules with applications to <i>C</i>*-modules
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.20, sa.11, 2021 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 20 Sayı: 11
- 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
- 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 pi-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 pi-Baer (S,R)-bimodules. Moreover, we specify subsets kappa 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.