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A Characterization of Weakly J(n)-Rings

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A Characterization of Weakly J(n)-Rings

Peter V. Danchev

Abstract: A ring R is called a J(n)-ring if there exists a natural number n ≥ 1 such that for each element r ∈ R the equality rn+1 = r holds and a weakly J(n)-ring if there exists a natural number n ≥ 1 such that for each element r ∈ R the equalities rn+1= r or rn+1= −r hold.

We completely describe both classes of these rings R for any n, thus considerably extending some well-known results in the subject, especially that of V. Peri´c in Publ. Inst. Math. Beograd (1983) as well as, in particular, the classical description of Boolean rings when n = 1.

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