Crossed Product-Like and Pre-Crystalline Graded Rings
We introduce crossed product-like rings, as a natural generalization of crystalline graded rings, and describe their basic properties. Furthermore, we prove that for certain pre-crystalline graded rings and every crystalline graded ring A, for which the base subring A_0 is commutative, each non-zero two-sided ideal has a nonzero intersection with C_A(A_0), i.e. the commutant of A_0 in A. We also s
