Prime divisors, asymptotic R-sequences and unmixed local rings
نویسندگان
چکیده
منابع مشابه
Prime divisors in Beatty sequences
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...
متن کاملThe Value Semigroups of Prime Divisors of the Second Kind in 2-dimensional Regular Local Rings
In this paper, it is shown that the value semigroup of a prime divisor of the second kind on a 2-dimensional regular local ring is symmetric. Further, a necessary and sufficient condition for two prime divisors of the second kind on a 2-dimensional regular local ring to have the same value semigroup is obtained.
متن کاملtλESSENTIAL 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...
متن کاملAsymptotic Prime Divisors of Torsion-free Symmetric Powers of Modules
Let R be a Noetherian ring, F := Rr and M ⊆ F a submodule of rank r. Let A∗(M) denote the stable value of Ass(Fn/Mn), for n large, where Fn is the nth symmetric power of Fn and Mn is the image of the nth symmetric power of M in Fn. We provide a number of characterizations for a prime ideal to belong to A∗(M). We also show that A∗(M) ⊆ A∗(M), where A∗(M) denotes the stable value of Ass(Fn/Mn).
متن کاملA Linear Function Associated to Asymptotic Prime Divisors
Let R be a Noetherian standard N d-graded ring and M,N finitely generated, N d-graded R-modules. Let I1, . . . , Is be finitely many homogeneous ideals of R. We show that there exist linear functions f, g : Ns → Nd such that the associated primes over R0 of [Exti(N,M/I1 1 · · · I ns s M)]m and [Tori(N,M/I n1 1 · · · I ns s M)]m are stable whenever m ∈ N d satisfies m ≥ f(n1, . . . , ns) and m ≥...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1985
ISSN: 0021-8693
DOI: 10.1016/0021-8693(85)90092-4