Throughout this paper R denotes an associative ring with identity and all modules are unitary. We use the symbol U(R) to denote the group of units of R and Id(R) the set of idempotents of R, Un(R) the set of elements which are the sum of n units of R, UΣ(R) the set of elements each of which is the sum of finitely many units in R, RE(R) (URE(R)) the set of regular (unit regular) elements of R, a...

For a ring R, R[x] is a left nearring under addition and substitution, and we denote it by (R[x], +, ◦). In this note, we show that if nil(R) is a locally nilpotent ideal of R, then nil(R[x], +, ◦) = nil(R)0[x], where nil(R) is the set of nilpotent elements of R and nil(R)0[x] is the 0-symmetric left nearring of polynomials with coefficients in nil(R). As a corollary, if R is a 2-primal ring, t...