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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The regular ring and the maximal ring of quotients of a finite Baer $^{\ast }$-ring


Author: Ernest S. Pyle
Journal: Trans. Amer. Math. Soc. 203 (1975), 201-213
MSC: Primary 16A28
DOI: https://doi.org/10.1090/S0002-9947-1975-0364338-9
MathSciNet review: 0364338
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Abstract: Necessary and sufficient conditions are obtained for extending the involution of a Baer $\ast$-ring to its maximal ring of quotients. Berberian’s 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.


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Keywords: Baer <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img8.gif" ALT="$\ast$">-ring, maximal ring of quotients, regular ring of a Baer <IMG WIDTH="16" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\ast$">-ring, <!– MATH $LP \sim RP$ –> <IMG WIDTH="92" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img7.gif" ALT="$LP \sim RP$">, (EP)-axiom, (SR)-axiom
Article copyright: © Copyright 1975 American Mathematical Society