A morphic ring of neat range one

• Published in: Algebra and Discrete Mathematics
• Date: 2015
• Main Authors: Pihura, O., Zabavsky, B.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/155168
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A morphic ring of neat range one / O. Pihura, B. Zabavsky // Algebra and Discrete Mathematics. — 2015. — Vol. 20, № 2. — С. 325-329. — Бібліогр.: 10 назв. — англ.

We show that a commutative ring R has neat range one if and only if every unit modulo principal ideal of a ring lifts to a neat element. We also show that a commutative morphic ring R has a neat range one if and only if for any elements a,b ∈ R such that aR=bR there exist neat elements s,t∈R such th...