The Maximal Graded Left Quotient Algebra of a Graded Algebra1)

We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms (of left A–modules) from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra, and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra. ¹⁾ Partially supported by the MCYT and Fondos FEDER, BFM2001–1938–C02–01 and the "Plan Andaluz de Investigación y Desarrollo Tecnológico", FQM 336 The first author partially supported by an FPU grant by the MECD (AP2001–1368)