We investigate chemical evolution in Milky Way-like galaxies based on the cold dark matter model in which cosmic structures form via hierarchical merging. We introduce chemical enrichment due to type Ia supernovae (SNe Ia) into the Mitaka semi-analytic galaxy formation model developed by Nagashima & Yoshii. For the first time we derive distributions of stellar metallicities and their ratios in Milky Way-like galaxies treating chemical enrichment due to SNe Ia in a hierarchical galaxy formation model self-consistently. As a first attempt, we assume all SNe Ia to have the same lifetime, and assume instantaneous recycling for type II supernovae (SNe II). We find that our model reproduces well the metal abundance ratio [O/Fe] against [Fe/H] and the {iron metallicity distribution function} in the solar neighborhood. This means that the so-called G-dwarf problem is resolved by the hierarchical formation of galaxies, and a gas infall term introduced in traditional monolithic collapse models to solve this problem is well explained by the mixture of some physical processes such as hierarchical merging of dark halos, gas cooling, energy feedback and injection of gas and metals into hot gas due to supernovae. Our model predicts more oxygen-enhanced stars in bulges at [Fe/H] $simeq 0$ than in disks. This trend seems to be supported by recent observations while they have still uncertainties. More data in number and accuracy will provide independent and important constraints on galaxy formation. (abridged)
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