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  1. No Access

    Article

    On left ideal essential extensions of rings

    The main goal of this paper is to extend Flanigan’s theorem in [4] concerning ideal essential extensions of rings to left ideal essential extensions. Moreover, we give new proofs of two Flanigan’s theorems and...

    M. Nowakowska, E. R. Puczyłowski in Acta Mathematica Hungarica (2020)

  2. 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)

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    Article

    Veldsman’s classes of associative rings

    The relation of being an ideal (left ideal, right ideal) of a ring is not transitive. Rings for which the transitivity does hold are called filial (left filial, right filial). In symbols, these are rings R such t...

    M. Nowakowska, E. R. Puczyłowski in Acta Mathematica Hungarica (2015)

  4. Article

    Open Access

    On 2-absorbing commutative semigroups and their applications to rings

    A commutative ring R is called 2-absorbing (Badawi in Bull. Aust. Math. Soc. 75:417–429, 2007) if for arbitrary elements a,b,c∈R, abc=0 if and only if ab=0 or bc=0 or ac=0. In this paper we study this concept in ...

    A. Yousefian Darani, E. R. Puczyłowski in Semigroup Forum (2013)

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    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)

  6. 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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  7. No Access

    Article

    On the structure of rings which are sums of two subrings

    We study the structure of rings that are sums of two subrings one of which is nil and the other reduced. Our main results concern the problem whether in this situation the nil subring must be an ideal.

    M. Kpczyk, E. R. Puczyłowski in Archiv der Mathematik (2004)

  8. No Access

    Article

    On essential extensions of reduced rings and domains

    A ring is said to be a left essential extension of a reduced ring (domain) if it contains a left ideal which is a reduced ring (domain) and intersects nontrivially every nonzero twosided ideal of the ring. We ...

    K. I. Beidar, Y. Fong, E. R. Puczyłowski in Archiv der Mathematik (2004)

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    Article

    A polynomial ring that is Jacobson radical and not nil

    In [1] Amitsur conjectured that if a polynomial ring in one indeterminate is Jacobson radical then it is a nil ring. We shall construct an example disproving this conjecture.

    Agata Smoktunowicz, E. R. Puczyłowski in Israel Journal of Mathematics (2001)

  10. No Access

    Article

    The nil radical of power series rings

    We describe the nil radical of power series rings in non-commuting indeterminates by showing that a series belongs to the radical if and only if the ideal generated by its coefficients is nilpotent. We also sh...

    E. R. Puczyłowski, Agata Smoktunowicz in Israel Journal of Mathematics (1999)

  11. No Access

    Article

    On radicals of rings which are sums of two subrings

    M. Kepczyk, E. R. Puczyłowski in Archiv der Mathematik (1996)

  12. No Access

    Article

    On general theory of radicals

    E. R. Puczyłowski in algebra universalis (1993)

  13. No Access

    Article

    A note on almost nilpotent rings

    E. R. Puczyłowski in Acta Mathematica Hungarica (1986)

  14. No Access

    Article

    On radicals of semigroup rings

    E. R. Puczyłowski in Acta Mathematica Academiae Scientiarum Hungarica (1982)

  15. No Access

    Article

    On unequivocal rings

    E. R. Puczyłowski in Acta Mathematica Academiae Scientiarum Hungarica (1980)