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UJ-rings are studied, i.e., ring in which all units can be presented in a form 1+x, for some x∈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 Köthe’s problem for 𝔽2-algebras.
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Koşan et al. (2017) studied this question.
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