Analyzing the structure of a class of linear automata over a ring % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbaGaa8Nwam % aaBaaaleaaieGacaGFWbWaaWbaaWqabeaacaGFRbaaaaWcbeaaaaa!391C! $$ Z_{p^k } $$

Basic finite-automaton characteristics are established for the class of all linear automata and information-lossless automata over a ring. The complexities of solving problems of parametric identification and initial-state identification are analyzed. The sets of fixed points for mappings realized by initial automata are characterized. Canonical forms are proposed for linear automata over the ring.