Lieutenant Governor Becky Skillman says even if it is not in an elected position, she would like to remain in politics.
Sue Ellspermann says schools need to emphasize art education, but Vi Simpson called for increased state funding for the arts.
The lieutenant governor debate held at the Indiana State Fair focused on agricultural issues.
Republican state delegates also nominated Tony Bennett and Greg Zoeller for another term in office.
The Republican nominee for lieutenant governor holds a doctorate in engineering.
Republican gubernatorial candidate Mike Pence will announce his choice for running mate Monday. A few names are being floated as possibilities.
Poltical talk has suggested Representative Sue Ellspermann although those involved say they cannot confirm or deny the speculation.