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  1. No Access

    Article

    On polynomial rings over nil rings in several variables and the central closure of prime nil rings

    We prove that the ring of polynomials in several commuting indeterminates over a nil ring cannot be homomorphically mapped onto a ring with identity, i.e. it is Brown-McCoy radical. It answers a question posed...

    M. Chebotar, W.-F. Ke, P.-H. Lee, E. R. Puczyłowski in Israel Journal of Mathematics (2018)

  2. No Access

    Article

    On Andrunakievich’s chain and Koethe’s problem

    In 1969 Andrunakievich asked whether one gets a ring without nonzero nil left ideals from an arbitrary ring R by factoring out the ideal A(R) which is the sum of all nil left ideals of R. Recently, it was shown t...

    M. A. Chebotar, P. -H. Lee, E. R. Puczyłowski in Israel Journal of Mathematics (2010)

  3. Article

    Open Access

    A note on termination of the Baer construction of the prime radical

    The well known Baer construction of the prime radical shows that the prime radical of an arbitrary ring is the union of the chain of ideals of the ring, constructed by transfinite induction, which starts with ...

    M. A. Chebotar, P. -H. Lee, E. R. Puczyłowski in Archiv der Mathematik (2010)

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  4. No Access

    Chapter and Conference Paper

    A Note on Polynomial Rings over Nil Rings

    Let R be a nil ring with p R = 0 for some prime number p. We show that the polynomial ring R[x,y] in two commuting indeterminates x, y over R cannot be homomorphicall...

    M. A. Chebotar, W. -F. Ke, P. -H. Lee, E. R. Puczyłowski in Modules and Comodules (2008)