Geodesic
Centres of Rank-Metric Completions
Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1134-1148

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we are primarily concerned with the behaviour of the centre with respect to the completion process for von Neumann regular rings at the pseudo-metric topology induced by a pseudo-rank function.Let R be a (von Neumann) regular ring, and N a pseudo-rank function (all terms left undefined here may be found in [6]). Then N induces a pseudo-metric topology on R, and the completion of R at this pseudo-metric, , is a right and left self-injective regular ring. Let Z( ) denote the centre of whatever ring is in the brackets. We are interested in the map .If R is simple, Z(R) is a field, so is discrete in the topology; yet Goodearl has constructed an example with Z(R) = R and Z(R) = C [5, 2.10]. There is thus no hope of a general density result. 
Handelman, David. Centres of Rank-Metric Completions. Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1134-1148. doi: 10.4153/CJM-1985-061-7
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[1] 1. Berberian, S. K., Baer *-rings (Springer-Verlag, Heidelberg/New York, 1972). Google Scholar | DOI

[2] 2. Blackadar, B. and Handelman, D., Dimension functions and traces on C*-algebras, J. of Functional Analysis 45 (1982), 297–340. Google Scholar

[3] 3. Effros, E. G., Handelman, D. E. and Shen, C.-L., Dimension groups and their affine representations, Amer. J. Math. 102 (1980), 385–407. Google Scholar

[4] 4. Farkas, D. and Snider, R., Locally finite dimensional algebras, Proc. Amer. Math. Soc. 81 (1981), 369–372. Google Scholar

[5] 5. Goodearl, K. R., Centers of completions of regular rings, Pacific J. Math. 76 (1978), 381–395. Google Scholar

[6] 6. Goodearl, K. R., von Neumann regular rings (Pitman, London, 1979). Google Scholar

[7] 7. Halperin, I., von Neumann's arithmetics of continuous rings, Acta sci. Math. 23 (1962), 1–17. Google Scholar

[8] 8. Halperin, I., Elementary divisors in von Neumann rings, Can. J. Math. 14 (1962), 39–44. Google Scholar

[9] 9. Menai, P., On tensor products of algebras being von Neumann regular or selfinjective, Comm. in Algebra 9 (1981), 691–7. Google Scholar

[10] 10. Menai, P. and Raphael, R., On epimorphism-final rings, preprint. Google Scholar

[11] 11. Renault, G., Algèbre non-commutative (Gauthier-Villars). Google Scholar

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