vuex: unknown getter: user

I'm experimenting with vuex and I was looking for best way to organize my vuex files I finished with something like this:

/src/store/user/state.js:

export default {
  state: {
    user: null
  }
}

/src/store/user/getters.js:

export default {
  getters: {
    user (state) {
      return state.user
    }
  }
}

/src/store/user/mutations.js:

export default {
  mutations: {
    'SET_USER' (state, user) {
      state.user = user
    }
  }
}

/src/store/user/actions.js

export default {
  actions: {
    loginUser ({ commit }, params) {
       commit('SET_USER', {id: 1})
    }
  }
}

/src/store/user/index.js

import state from './state'
import getters from './getters'
import actions from './actions'
import mutations from './mutations'

export default {
  state,
  getters,
  actions,
  mutations
}

/src/store/index.js:

import Vue from 'vue'
import Vuex from 'vuex'
import user from './user'

Vue.use(Vuex)

export default new Vuex.Store({
  modules: {
    user
  }
})

When I load my code it returns in console following error:

vuex: unknown getter: user