Let U , V , and W be multiplicative unitaries coming from discrete Kac systems such that W is an amenable normal submultiplica-tive unitary of V with quotient U. We define notions for right-Hilbert bimodules of coactions of SV andˆSV , their restrictions to SW andˆSU , their dual coactions, and their full and reduced crossed products. If N (A) denotes the imprimitivity bimodule associated to a ...

For a monoid M , we introduce linear M-Armendariz rings, which are generalization of M-Armendariz rings and linear Armendariz rings; and investigate their properties. Every reduced ring is linear M-Armendariz, for any unique product monoid. We show that if M be a monoid and R be a right ore ring with classical right quotient ring Q. Then R is linear M-Armendariz if and only if Q is linear M-Arm...

In this paper, we prove that any BL-general fuzzy automaton (BL-GFA) and its quotient have the same behavior. In addition, we obtain the minimal quotient BL-GFA and minimal quotient transformation of the BL-GFA, considering the notion of maximal admissible partition. Furthermore, we show that the number of input symbols and time complexity of the minimal quotient transformation of a BL-GFA are ...