Upon the death of a married person, one-half of the property to which this chapter applies is the property of the surviving spouse and is not subject to testamentary disposition by the decedent or distribution under the laws of succession of this state. The other half of the property to which this chapter applies is the property of the decedent and is subject to testamentary disposition or distribution under the laws of succession of this state. With respect to property to which this chapter applies, the one-half of the property that is the property of the decedent is not subject to the surviving spouse's right to elect against the will.