منابع مشابه
Gin AND Lex OF CERTAIN MONOMIAL IDEALS
Let A = K[x1, . . . , xn] denote the polynomial ring in n variables over a field K of characteristic 0 with each deg xi = 1. Given arbitrary integers i and j with 2 ≤ i ≤ n and 3 ≤ j ≤ n, we will construct a monomial ideal I ⊂ A such that (i) βk(I) < βk(Gin(I)) for all k < i, (ii) βi(I) = βi(Gin(I)), (iii) βl(Gin(I)) < βl(Lex(I)) for all l < j and (iv) βj(Gin(I)) = βj(Lex(I)), where Gin(I) is t...
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A one-sided ideal of a ring has the insertion of factors property (or simply, IFP) if implies r for . We say a one-sided ideal of has the weakly IFP if for each , implies , for some non-negative integer . We give some examples of ideals which have the weakly IFP but have not the IFP. Connections between ideals of which have the IFP and related ideals of some ring extensions a...
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In order that <r0 ^ 0 , in which case (3.1) will converge in the right half of the s-plane, it is sufficient that vn tend to infinity faster than log n. The argument used to complete the proof of Theorem 2 is the same as the one used above in connection with Theorem 1. Notice that if {vn+i — vn} is not a null sequence, then vn tends to infinity faster than log n. This eliminates the extra restr...
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The ideal I 1 generated by the 2 2 quantum minors in the coordinate algebra of quantum matrices, O q (M m;n (k)), is investigated. Analogues of the First and Second Fundamental Theorems of Invariant Theory are proved. In particular, it is shown that I 1 is a completely prime ideal, that is, O q (M m;n (k))=I 1 is an integral domain, and that O q (M m;n (k))=I 1 is the ring of coinvariants of a ...
متن کاملOn the Homological Dimension of Certain Ideals
1. Introduction. We present two closely related results connecting homological dimension theory and the ideal theory of noetherian rings. The first, Proposition 4.1, asserts that the only ideals of finite homological dimension in a local ring whose associated prime ideals all have grade one are of the form aR:bR. The second, Proposition 4.3, asserts that if R is a noetherian integral domain, th...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1990
ISSN: 0022-4049
DOI: 10.1016/0022-4049(90)90123-y