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The subalgebra of the tautological ring of the moduli of curves of compacttype generated by the kappa classes is studied in all genera. Relations,constructed via the virtual geometry of the moduli of stable quotients, areused to obtain minimal sets of generators. Bases and Betti numbers of the kapparings are computed. A universality property relating the higher genus kapparings to the genus 0 rings is stated and proved in a sequel. The lambda_gformula for Hodge integrals arises as the simplest consequence.

The kappa ring of the moduli of curves of compact type: I