TY - JOUR
T1 - Quotient rings and f-radical extensions of rings
AU - Chuang, Chen Lian
AU - Lee, Tsiu Kwen
AU - Liu, Cheng-Kai
PY - 2009/9/1
Y1 - 2009/9/1
N2 - 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 (X1, . . . , Xt)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.
AB - 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 (X1, . . . , Xt)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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U2 - 10.1080/00927870802241170
DO - 10.1080/00927870802241170
M3 - Article
AN - SCOPUS:70449581252
VL - 37
SP - 2933
EP - 2944
JO - Communications in Algebra
JF - Communications in Algebra
SN - 0092-7872
IS - 9
ER -