Non-commutative regular local rings of dimension 2. II
In an earlier paper [ibid. 115, No.1, 219-237 (1988; Zbl 0648.16010)] the author constructed a prime ring T by localising at the maximal Ore set of regular elements modulo P, where P is a prime ideal of a noetherian ring R that is generated by two elements x,y such that y is a nonzero divisor, \(yR=Ry\), x is a nonzero divisor modulo yR and \(P=xR+yR=Rx+Ry\). He established various properties of T and in the present paper continues this theme. The Jacobson radical of T is yT and T/yT is semiprime; the number of prime ideals minimal over yT is denoted n(T). Two rings R and S are said to be matrix equivalent if there are rings \(R=R_ 0,R_ 1,...,R_ m=S\) such that for each pair \(\{R_ i,R_{i+1}\}\) one ring is a full matrix ring over the other. One of the main results in the paper is that the ring T is matrix equivalent to an n(T)\(\times n(T)\) tiled matrix ring over a domain D with properties similar to T but \(n(D)=1\).
scientific article; zbMATH DE number 4093672