On UJ-rings

Abstract

UJ-rings are studied, i.e., ring in which all units can be presented in a form 1+x, for some xJ(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 ?(2)-algebras.