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In the present note we study the properties of weak
Armendariz rings, and the connections among weak Armendariz rings,
Armendariz rings, reduced rings and IFP rings. We prove that a right
Ore ring R is weak Armendariz if and only if so is Q, where Q
is the classical right quotient ring of R. With the help of this
result we can show that a semiprime right Goldie ring R is weak
Armendariz if and only if R is Armendariz if and only if R is reduced if and only if R is IFP
if and only if Q is a finite direct product of division rings, obtaining a
simpler proof of Lee and Wong's result. In the process we construct
a semiprime ring extension that is infinite dimensional, from given
any semiprime ring. We next find more examples of weak Armendariz
rings.
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참고문헌 (16)
참고문헌 신청
C. H / 2002 / Armendariz rings and semicommutative rings / Comm. Algebra 30 (2) : 751 ~ 761
C. Huh / 2002 / p.p. rings and generalized p.p. rings / J. Pure Appl. Algebra 167 (1) : 37 ~ 52
D. D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Algebra 26 (7) : 2265 ~ 2272
E. P. Armendariz / 1974 / A note on extensions of Baer and P.P.-rings / J. Austral. Math. Soc. 18 : 470 ~ 473
G. Shin / 1973 / Prime ideals and sheaf representation of a pseudo symmetric ring / Trans. Amer. Math. Soc. 184 : 43 ~ 60
C. Huh / 2002 / p.p. rings and generalized p.p. rings / J. Pure Appl. Algebra 167 (1) : 37 ~ 52
D. D. Anderson / 1998 / Armendariz rings and Gaussian rings / Comm. Algebra 26 (7) : 2265 ~ 2272
E. P. Armendariz / 1974 / A note on extensions of Baer and P.P.-rings / J. Austral. Math. Soc. 18 : 470 ~ 473
G. Shin / 1973 / Prime ideals and sheaf representation of a pseudo symmetric ring / Trans. Amer. Math. Soc. 184 : 43 ~ 60
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