Multiplicative Ideal Theory in Noncommutative Rings

AKALAN E., Marubayashi H.

Conference on Arithmetic and Ideal Theory of Rings and Semigroups, Graz, Austria, 22 - 24 September 2014, vol.170, pp.1-21 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 170
  • Doi Number: 10.1007/978-3-319-38855-7_1
  • City: Graz
  • Country: Austria
  • Page Numbers: pp.1-21
  • Hacettepe University Affiliated: Yes


The aim of this paper is to survey noncommutative rings from the viewpoint of multiplicative ideal theory. The main classes of rings considered are maximal orders, Krull orders (rings), unique factorization rings, generalized Dedekind prime rings, and hereditary Noetherian prime rings. We report on the description of reflexive ideals in Ore extensions and Rees rings. Further we give necessary and sufficient conditions (or sufficient conditions) for well-known classes of rings to be maximal orders, and we propose a polynomial-type generalization of hereditary Noetherian prime rings.