Mathematics Faculty Articles

Title

αcc-Baer Rings

Document Type

Article

Publication Date

3-2015

Publication Title

Mathematica Slovaca

Keywords

αcc-Baer rings, α-Baer rings, αcc-disconnected, αcc-Baer hull, Baer-rings, f-rings

ISSN

0139-9918

Volume

65

Issue/No.

2

First Page

371

Last Page

386

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.

Comments

©2015 Mathematical Institute Slovak Academy of Sciences

DOI

10.1515/ms-2015-0029

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Peer Reviewed

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