Stable range one for rings with central units

• Type: Article in International Scientific Journal
• Date: 2020

Authors

Paula A.A.B. Carvalho (Author) FCUP; Christian Lomp (Author) FCUP; Matczuk, J (Author) Other

Journal

Title: Communications in Algebra

Vol. 48

Pages: 4767-4773

ISSN: 0092-7872

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Scientific classification

CORDIS: Physical sciences > Mathematics > Algebra

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-00S-90G

DOI: 10.1080/00927872.2020.1770275

Abstract (EN): The purpose of this paper is to give a partial positive answer to a question raised by Khurana et al. as to whether a ringRwith stable range one and central units is commutative. We show that this is the case under any of the following additional conditions:Ris semiprime orRis one-sided Noetherian orRhas unit-stable range 1 orRhas classical Krull dimension 0 orRis an algebra over a fieldKsuch thatKis uncountable andRhas only countably many primitive ideals orRis affine and eitherKhas characteristic 0 or has infinite transcendental degree over its prime subfield or is algebraically closed. However, the general question remains open.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 7