Now showing items 1-6 of 6

    • Almost unit-clean rings 

      Chen, H.; Köse, H.; Kurtulmaz, Yosum (Editura Academiei Romane, 2019)
      A ring R is almost unit-clean provided that every element in R is equivalent to the sum of an idempotent and a regular element. We investigate conditions under which a ring is almost unit-clean. We prove that every ring ...
    • Local comparability of exchange ideals 

      Köse, H.; Kurtulmaz, Yosum; Chen, H. (Hacettepe University, 2019)
      An exchange ideal I of a ring R is locally comparable if for every regular x ∈ I there exists a right or left invertible u ∈ 1+I such that x = xux. We prove that every matrix extension of an exchange locally comparable ...
    • A nil approach to symmetricity of rings 

      Üngör, B.; Köse, H.; Kurtulmaz, Yosum; Harmancı, A. (Allahabad Mathematical Society, 2018)
      We introduce a weakly symmetric ring which is a generalization of a symmetric ring and a strengthening of both a GWS ring and a weakly reversible ring, and investigate properties of the class of this kind of rings. A ring ...
    • Reflexivity of rings via nilpotent elements 

      Harmancı, A.; Köse, H.; Kurtulmaz, Yosum; Üngör, B. (Union Matematica Argentina, 2020)
      An ideal I of a ring R is called left N-reflexive if for any a ∈ nil(R) and b ∈ R, aRb ⊆ I implies bRa ⊆ I, where nil(R) is the set of all nilpotent elements of R. The ring R is called left N-reflexive if the zero ideal ...
    • Rings having normality in terms of the Jacobson radical 

      Köse, H.; Kurtulmaz, Yosum; Harmancı, A. (Springer, 2020)
      A ring R is defined to be J-normal if for any a,r∈Ra,r∈R and idempotent e∈Re∈R, ae=0ae=0 implies Rera⊆J(R)Rera⊆J(R), where J(R) is the Jacobson radical of R. The class of J-normal rings lies between the classes of weakly ...
    • Semicommutativity of amalgamated rings 

      Köse, H.; Kurtulmaz, Yosum; Üngör, B.; Harmancı, A. (Journal of Mathematical Research with Applications, 2018)
      In this paper, we study some cases when an amalgamated construction A ◃▹f I of a ring A along an ideal I of a ring B with respect to a ring homomorphism f from A to B, is prime, semiprime, semicommutative, nil-semicommutative ...