Browsing by Author "Birkenmeier, Gary F."
Now showing 1 - 3 of 3
- Results Per Page
- Sort Options
Publication A partial order on subsets of baer bimodules with applications to c*-modules(World Scientific Publ Co Pte Ltd, 2021-11-01) Birkenmeier, Gary F.; Kara, Yeliz; KARA ŞEN, YELİZ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-8001-6082; AAG-8304-2021In 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.Publication π-endo Baer modules(Taylor & Francis, 2020-03-03) Birkenmeier, Gary F.; Kara, Yeliz; Tercan, Adnan; KARA ŞEN, YELİZ; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-8001-6082; AAG-8304-2021Let N be a submodule of a right R-module M-R, and Then N is said to be projection invariant in M, denoted by if for all We call M-R ?-endo Baer, denoted ?-e.Baer, if for each there exists such that where denotes the left annihilator of N in H. We show that this class of modules lies strictly between the classes of Baer and quasi-Baer modules introduced in 2004 by Rizvi and Roman. Several structural properties are developed. In contrast to the Baer modules of Rizvi and Roman, the free modules of a Baer ring are ?-e.Baer. Moreover, (co-) nonsingularity conditions are introduced which enable us to extend the Chatters-Khuri result (connecting the extending and Baer conditions in a ring) to modules. We provide examples to illustrate and delimit our results.Publication Π-Rickart rings(World Scientific Publ Co Pte, 2021-08-01) Birkenmeier, Gary F.; Tercan, Adnan; Kara, Yeliz; KARA ŞEN, YELİZ; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-8001-6082In this paper, we introduce and investigate three new versions of the Rickart condition for rings. These conditions, as well as, three new corresponding regularities are defined using projection invariance. We show how these conditions relate to each other as well as their connections to the well-known Baer, Rickart, quasi-Baer, p.q.-Baer, regular, and biregular conditions. Applications to polynomial extensions and to triangular and full matrix rings are provided. Examples illustrate and delimit results.