Quotient Rings and f-Radical Extensions of Rings |
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Authors: | Chen-Lian Chuang ♯ Tsiu-Kwen Lee ♯ |
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Institution: | Department of Mathematics , National Taiwan University , Taipei, Taiwan |
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Abstract: | By testing quotient rings, we give another viewpoint concerning the relationship between PI and Goldie properties, etc., and f-radical extensions of rings. The main result proved here is as follows: Let R be a prime algebra without nonzero nil right ideals. Suppose that R is f-radical over a subalgebra A, where f(X 1,…, X t ) is a multilinear polynomial, not an identity for p × p matrices in case char R = p > 0. Suppose that f is not power-central valued in R. Then the maximal ring of right (left) quotients of A coincides with that of R. Moreover, R is right Goldie if and only if A is. |
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Keywords: | f-Radical extension GPI PI Prime algebra Quotient ring |
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