Article
αcc-Baer Rings
Mathematica Slovaca
Document Type
Article
Publication Date
3-1-2015
Keywords
- αcc-Baer rings,
- α-Baer rings,
- αcc-disconnected,
- αcc-Baer hull,
- Baer-rings,
- f-rings
Disciplines
Abstract
Let α denote an infinite cardinal or ∞ which is used to signify no cardinal constraint. This work introduces the concept of an αcc-Baer ring and demonstrates that a commutative semiprime ring A with identity is αcc-Baer if and only if Spec(A) is αcc-disconnected. Moreover, we prove that for each commutative semprime ring A with identity there exists a minimum αcc-Baer ring of quotients, which we call the αcc-Baer hull of A. In addition, we investigate a variety of classical α-Baer ring results within the contexts of αcc-Baer rings and apply our results to produce alternative proofs of some classical results such as A is α-Baer if and only if Spec(A) is α-disconnected. Lastly, we apply our results within the contexts of archimedean f-rings.
DOI
10.1515/ms-2015-0029
Citation Information
Ricardo Enrique Carrera, Wolf Iberkleid, Ramiro Lafuente-Rodriguez and Warren William McGovern. "αcc-Baer Rings" Mathematica Slovaca Vol. 65 Iss. 2 (2015) p. 371 - 386 ISSN: 0139-9918 Available at: http://works.bepress.com/wolf-iberkleid/17/
©2015 Mathematical Institute Slovak Academy of Sciences