Countably coverable rings. Issue 7 (3rd July 2023)

• Record Type: Journal Article
• Authors: Oman, Greg; Werner, Nicholas J.
• Is Part Of: Communications in algebra. Volume 51:Issue 7(2023)
• Page Start: 2748
• Page End: 2758
• Publication Date: 2023-07-03
• Subjects: Algebraically closed field -- coverable ring -- localization -- transcendence basis; Primary: 13A70 -- 13E05 -- Secondary: 13G05; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2023.2172177
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: Let R be an associative ring. Then R is said to be coverable provided R is the union of its proper subrings (which we do not require to be unital even if R is so). One verifies easily that R is coverable if and only if R is not generated as a ring by a single element. In case R can be expressed as the union of a finite number of proper subrings, the least such number is called the covering number of R . Covering numbers of rings have been studied in a series of recent papers. The purpose of this note is to study rings which can be covered by a countable collection of subrings.