On UJ-rings
M.Tamer Kosan, Andre Leroy, Jerzy Matczuk

TL;DR
This paper investigates UJ-rings, where all units are of the form 1 + x with x in the Jacobson radical, exploring their properties and how they behave under algebraic constructions, linking to Kothe's problem.
Contribution
It establishes the equivalence between lifting the UJ property to polynomial rings and Kothe's problem for F_2-algebras, providing new insights into ring theory.
Findings
UJ-rings have specific unit structures related to the Jacobson radical
Lifting the UJ property to polynomial rings relates to Kothe's problem
The behavior of UJ-rings under algebraic constructions is characterized
Abstract
UJ-rings are studied, i.e. ring in which all units can be presented in a form 1 + x, for some x\in J(R). The behavior of UJ-rings under various algebraic construction is investigated. In particular, it is shown that the problem of lifting the UJ property from a ring R to the polynomial ring R[x] is equivalent to the Kothe's problem for F_2-algebras.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Algebra and Logic · Commutative Algebra and Its Applications
