On the Property (PU) for *-Regular Rank Rings
Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 21-38

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In this paper we consider an irreducible *-regular ring with order k for some k≥4. If is also a Baer ring it is a rank ring. Our first result is:Theorem 1.3. Let be an irreducible *-regular Baer ring with order k for some k≥4. The following are equivalent.
Burke, John L. On the Property (PU) for *-Regular Rank Rings. Canadian mathematical bulletin, Tome 19 (1976) no. 1, pp. 21-38. doi: 10.4153/CMB-1976-004-x
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[1] 1. Halperin, Israel, Regular rank rings, Can. J. Math. 17 (1965), 709–719. Google Scholar

[2] 2. Halperin, Israel, Extension of the rank function, Studia Math. 27 (1966), 325–335. Google Scholar

[3] 3. Halperin, Israel, von Neumann’s manuscript on the inductive limit of regular rings. Can. J. Math. 20 (1968), 477–483. Google Scholar

[4] 4. Kaplansky, Irving, Any orthocomplemented complete modular lattice is a continuous geometry, Ann. of Math. 61 (1955), 524–541. Google Scholar

[5] 5. Kaplansky, Irving, Rings of operators (Benjamin, New York, 1968). Google Scholar

[6] 6. von Neumann, John, Continuous geometries with a transition probability, unpublished manuscript (reviewed by Israel Halperin in the Collected Works of John von Neumann, Pergamon, Elmsford, N.Y., 1962). Google Scholar

[7] 7. von Neumann, John, Continuous geometry (Princeton University Press, Princeton, 1960). Google Scholar

[8] 8. von Neumann, John, The non-isomorphism of certain continuous rings, Ann. of Math. 67 (1958), 485–496. Google Scholar

[9] 9. Prijatelj, N. and Vidav, I., On special -regular rings, Michigan Math. J. 18 (1971), 213–221. Google Scholar

[10] 10. Vidav, I., On some *-regular rings, Acad. Serbe Sci. Publ. Inst. Math. 13 (1959), 73–80. Google Scholar

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