On Free Ring Extensions of Degree N
نویسنده
چکیده
Nagahara and Kishimoto [i] studied free ring extensions B(x) of degree n n for some integer n over a ring B with i, where x b, cx xp(c) for all c and n-I some b in B (p automorphism of B), and {i, x x is a basis. Parimala and Sridharan [2], and the author investigated a class of free ring extensions called generalized quaternlon algebras in which b -I and p is of order 2. The purpose of the present paper is to generalize a characterization of a generalized quaternion algebra to a free ring extension of degree n in terms of the Azumaya algebra. Also, it is shown that a one-to-one correspondence between the set of invariant ideals of B under p and the set of ideals of B(x) leads to a relation of the Galois extension B over an invariant subring under to the center of B. KEY WODS AND PHRASES. Free ring extensions, separable algebras, Azumaya algebras, Gaois extensions. 198u MATHEMATICS SUBJECT CLASSIFICATION CODES: 16A16, 13A20, 13B05.
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