A note on utumi quotient rings?
Resource
Communications in Algebra 28 (9): 4089-4103
Journal
Communications in Algebra
Pages
4089-4103
Date Issued
2000
Date
2000
Author(s)
Lee, T. K.
Abstract
Abstract Let R be a ring and ρ a right ideal of R with zero right annihilate. Then ρ and R have the same left Utumi quotient ring. We study the lifting properties of GPIs and some chain conditions inherited by such right ideals. Next, we prove a generalization of Chatters’ theorem. Precisely, we show that if R is a right nonsingular ring with finite right Goldie dimension and possesses a right ideal ρ such that both ρ and l R(ρ) are PI-rings, then the right Utumi quotient ring of R is also a Pi-ring. Keywords: PIGPIUtumi quotient ringleft Goldie ring
Type
journal article
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