The reduction theorem for algebras of one-sided subshifts over arbitrary alphabets. - Bagio, Dirceu; Gil-Canto, Cristóbal; Gonçalves, Daniel; Royer, Danilo (Springer, 2024)
Let R be a commutative unital ring, X a subshift, and A_R(X) the corresponding unital subshift algebra. We establish the reduction theorem for A_R(X). As a consequence, we obtain a Cuntz-Krieger uniqueness theorem for A_R(X) and we show that A_R(X) is semiprimitive (resp. semiprime) whenever R is a field (resp. a domain).
Keywords: Algebra lineal; Subshift algebra; Reduction theorem; Partial skew group rings; Semiprime rings; Semiprimitive rings