Some constructions of rings
Starting from a Dedekind domain R and a fractional ideal I of R one may construct the so-called generalised Rees ring as follows: \[ \check R(I)=...\oplus I^{-n}\oplus...\oplus I^{-1}\oplus R\oplus I\oplus...\oplus I^ n\oplus... \] The concept of a generalised Rees ring underwent consequent generalisations both in the commutative case and in the non-commutative case and it turned out that these constructions of graded nature also have very nice ungraded properties. In constructing those rings, the author obtains new examples of Goldie rings, maximal orders, tame orders in the sense of R. Fossum, Krull orders in the PI case or the general case, and \(\nu\) HC-orders in the sense of H. Fujita or H. Marubayashi. Three major classes are considered: strong Rees rings, divisorial Rees rings, scaled Rees rings; in each of these classes particular attention is payed to the commutative case, the PI case and the general case.
scientific article; zbMATH DE number 3843934
scientific article