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Let R be a ring and I be a proper ideal of R. For the case
of R being commutative, Anderson proved that (*) there are only finitely
many prime ideals minimal over I whenever every prime ideal minimal
over I is finitely generated. We in this note extend the class of rings
that satisfies the condition (∗) to noncommutative rings, so called homomorphically
IFP, which is a generalization of commutative rings. As
a corollary we obtain that there are only finitely many minimal prime
ideals in the polynomial ring over R when every minimal prime ideal of
a homomorphically IFP ring R is finitely generated
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참고문헌 (9)
참고문헌 신청
A. W. Chatters / 1990 / On right duo p.p. rings / Glasgow Mathematical Journal 32 (2) : 221 ~ 225
D. D. Anderson / 1994 / A note on minimal prime ideals / Proceedings of the American Mathematical Society 122 (1) : 13 ~ 14
G. Shin / 1973 / Prime ideals and sheaf representation of a pseudo symmetric ring / Transactions of the American Mathematical Society 184 : 43 ~ 50
H. E. Bell / 1970 / Near-rings in which each element is a power of itself / BULLETIN of the Australian Mathematical Society 2 : 363 ~ 368
J. C. McConnell / 1987 / Noncommutative Noetherian Rings / John Wiley & Sons, Ltd.
D. D. Anderson / 1994 / A note on minimal prime ideals / Proceedings of the American Mathematical Society 122 (1) : 13 ~ 14
G. Shin / 1973 / Prime ideals and sheaf representation of a pseudo symmetric ring / Transactions of the American Mathematical Society 184 : 43 ~ 50
H. E. Bell / 1970 / Near-rings in which each element is a power of itself / BULLETIN of the Australian Mathematical Society 2 : 363 ~ 368
J. C. McConnell / 1987 / Noncommutative Noetherian Rings / John Wiley & Sons, Ltd.
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