U–essential prime divisors and sequences over an ideal
نویسندگان
چکیده
منابع مشابه
tλESSENTIAL PRIME DIVISORS AND SEQUENCES OVER AN IDEAL
All rings in this paper are assumed to be commutative with identity, and they will generally also be Noetherian. In several recent papers the asymptotic theory of ideals in Noetherian rings has been introduced and developed. In this new theory the roles played in the standard theory by associated primes, i?-sequences, classical grade, and Cohen-Macaulay rings are played by, respectively, asympt...
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Let $I$ denote an ideal of a Noetherian ring $R$. The purpose of this article is to introduce the concepts of quintasymptotic sequences over $I$ and quintasymptotic cograde of $I$, and to show that they play a role analogous to quintessential sequences over $I$ and quintessential cograde of $I$. We show that, if $R$ is local, then the quintasymptotic cograde of $I$ is una...
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We study the values of arithmetic functions taken on the elements of a non-homogeneous Beatty sequence αn+ β , n= 1,2, . . . , where α,β ∈R, and α > 0 is irrational. For example, we show that ∑ n N ω ( αn+ β )∼N log logN and ∑ n N (−1)Ω( αn+β ) = o(N), where Ω(k) and ω(k) denote the number of prime divisors of an integer k = 0 counted with and without multiplicities, respectively. © 2006 Elsevi...
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let $i$ denote an ideal of a noetherian ring $r$. the purpose of this article is to introduce the concepts of quintasymptotic sequences over $i$ and quintasymptotic cograde of $i$, and to show that they play a role analogous to quintessential sequences over $i$ and quintessential cograde of $i$. we show that, if $r$ is local, then the quintasymptotic cograde of $i$ is una...
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We consider the primes which divide the denominator of the x-coordinate of a sequence of rational points on an elliptic curve. It is expected that for every sufficiently large value of the index, each term should be divisible by a primitive prime divisor, one that has not appeared in any earlier term. Proofs of this are known in only a few cases. Weaker results in the general direction are give...
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1986
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s002776300000057x