Delaware requires any real estate salesperson applicant to demonstrate good character, with no criminal conviction records related to their ability to practice real estate. Your application will be denied for crimes such as murder, reckless endangerment, sex crimes, kidnapping, arson, burglary, robbery, theft, extortion, identity theft, fraud, child endangerment, or perjury.
You can find the full list of reasons for denial under the rules and regulations for the Real Estate Commission, Chapter 24, Statute 2906, Section 16, Crimes Related to the Practice of Real Estate Services.