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 Minnesota. The other one-half of that property is the property of the decedent and is subject to testamentary disposition or distribution under the laws of succession of Minnesota. With respect to property to which this chapter applies, the one-half of the property which is the property of the decedent is not subject to the surviving spouse’s right to elect against the will and is not included in the decedent’s net estate which is subject to the elective share of the surviving spouse.