For a henselian local ringR, Azurnaya [3] proved that every module-finiteR-algebraRwithR/RadAseparable admits an inertial algebra, that is. a separable subalgebraBwithB+ RadA=A, and he showed thatBis unique up to conjugation. This fundamental theorem has been a starting point for intensive research on inertial algebras, with major contributions by Ingraham [10, 16. 17, 18], Brown [7, 8, 9, 10], Kirkman [19], Wehlen [25, 26, 27], Cipolla [11, 12], Deneen [14]. and others.