Towards a Goldie theory for Jordan pairs
The paper under review is devoted to start a Goldie theory for linear Jordan pairs. To do this, a notion of order is defined and it is shown the compatibility with the previous concept of order in Jordan algebras, introduced by \textit{E. I. Zelmanov} [Sib. Math. J. 28, 899-906 (1987); translation from Sib. Mat. Zh. 28, No. 6, 44-52 (1987; 638.17012) and Sib. Math. J. 29, 567-573 (1988); translation from Sib. Mat. Zh. 29, No. 4, 68-74 (1988; Zbl 0663.17016)]. The main result asserts that a linear Jordan pair \(V\) which is an order in a nondegenerate and locally artinian linear Jordan pair \(W\) is nondegenerate, satisfies the ascending chain condition on annihilators of elements and has finite Goldie dimension. Moreover, \(V\) is strongly prime if and only if \(W\) is simple.
scientific article; zbMATH DE number 1135226