The regular ring and the maximal ring of quotients of a finite Baer $^{\ast }$ring
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 by Ernest S. Pyle PDF
 Trans. Amer. Math. Soc. 203 (1975), 201213 Request permission
Abstract:
Necessary and sufficient conditions are obtained for extending the involution of a Baer $\ast$ring to its maximal ring of quotients. Berberianβs construction of the regular ring of a Baer $\ast$ring is generalized and this ring is identified (under suitable hypotheses) with the maximal ring of quotients.References

S. K. Berberian, The regular ring a finite $A{W^ \ast }$algebra, Ph.D. Thesis, University of Chicago, Chicago, III., 1955.
 S. K. Berberian, The regular ring of a finite Baer $^{\ast }$ring, J. Algebra 23 (1972), 35β65. MR 308179, DOI 10.1016/00218693(72)900440 β, Baer $^\ast$rings, SpringerVerlag, New York, 1972.
 Carl Faith, Lectures on injective modules and quotient rings, Lecture Notes in Mathematics, No. 49, SpringerVerlag, BerlinNew York, 1967. MR 0227206, DOI 10.1007/BFb0074319
 R. E. Johnson, The extended centralizer of a ring over a module, Proc. Amer. Math. Soc. 2 (1951), 891β895. MR 45695, DOI 10.1090/S00029939195100456959
 Irving Kaplansky, Any orthocomplemented complete modular lattice is a continuous geometry, Ann. of Math. (2) 61 (1955), 524β541. MR 88476, DOI 10.2307/1969811
 Irving Kaplansky, Rings of operators, W. A. Benjamin, Inc., New YorkAmsterdam, 1968. MR 0244778 E. S. Pyle, On maximal rings of quotients of finite Baer $^\ast$rings, Ph.D. Thesis, University of Texas, Austin, Tex., 1972. J.E. Roos, Sur lβanneau maximal de fractions des $A{W^ \ast }$algbrees et des anneaux de Baer, C. R. Acad. Sci. Paris SΓ©r. AB 266 (1968), A120A123. MR 39 #6093.
 Yuzo Utumi, On quotient rings, Osaka Math. J. 8 (1956), 1β18. MR 78966
 Y. Utumi, On rings of which any onesided quotient rings are twosided, Proc. Amer. Math. Soc. 14 (1963), 141β147. MR 142568, DOI 10.1090/S00029939196301425686
Additional Information
 © Copyright 1975 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 203 (1975), 201213
 MSC: Primary 16A28
 DOI: https://doi.org/10.1090/S00029947197503643389
 MathSciNet review: 0364338