Baer-环构成条件的反例探讨

The Counterexample of Constistic Condition for Baer Rings

研究了Baer-环的若干性质和构成条件.在文献[1]给出素PI-环S=Mat2(Z2[x])的子环R是素PI-环但不是Baer-环这一反例的基础上,进一步证明了对任意素数p,R是素PI-环,但不是Baer-环,从而扩展了文献[1]给出的反例的条件.

We study several properties of Baer ring and the conditions for which ring may be Baer. Due to [1], the subring R of prime PI ring S=Mat2（Z2[x]） is prime PI ring, but it can not be Baer. Furthermore, under this counterexample, we prove that R is prime PI ring, but it is not Baer for any prime p. Accordingly, we extend the class of counterexample of Baer rings.