We present a symmetric version of a normed algebra of quotients for each ultraprime normed algebra. In addition, a C*-algebra of quotients of an arbitrary C*-algebra is introduced. 1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): primary 46 H 20; secondary, 46 L 05, 47 B 99, 16 A 08.
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