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1.
Let T be a complete local (Noetherian) ring with maximal ideal M, P a nonmaximal ideal of T, and C = {Q 1, Q 2,…} a (nonempty) finite or countable set of nonmaximal prime ideals of T. Let {p 1, p 2,…} be a set of nonzero regular elements of T, whose cardinality is the same as that of C. Suppose that p i ∈ Q j if and only if i = j. We give conditions that ensure there is an excellent local unique factorization domain A such that A is a subring of T, the maximal ideal of A is M ∩ A, the (M ∩ A)-adic completion of A is T, and so that the following three conditions hold: (1) p i ∈ A for every i; (2) A ∩ P = (0), and if J is a prime ideal of T with J ∩ A = (0), then J ? P or J ? Q i for some i; (3) for each i, p i A is a prime ideal of A, Q i ∩ A = p i A, and if J is a prime ideal of T with J ? Q i , then J ∩ A ≠ p i A. 相似文献
2.
T. Guédénon 《代数通讯》2013,41(12):4403-4413
ABSTRACT Let k be a field, R an associative k-algebra with identity, Δ a finite set of derivations of R, and R[Θ1, δ1] ··· [Θ n , δ n ] an iterated differential operator k-algebra over R such that δ j (Θ i ) ∈ R[Θ1, δ1] ··· [Θ i?1, δ i?1]; 1 ≤ i < j ≤ n. If R is Noetherian Δ-hypercentral, then every prime ideal P of A is classically localizable. The aim of this article is to show that under some additional hypotheses on the Δ-prime ideals of R, the local ring A P is regular in the sense of Robert Walker. We use this result to study the catenarity of A and to compute the numbers μ i of Bass. Let g be a nilpotent Lie algebra of finite dimension n acting on R by derivations and U(g) the enveloping algebra of g. Then the crossed product of R by U(g) is an iterated differential operator k-algebra as above. In this particular case, our results are known if k has characteristic zero. 相似文献
3.
Let 𝒜 = (A n ) n≥0 be an ascending chain of commutative rings with identity, S ? A 0 a multiplicative set of A 0, and let 𝒜[X] (respectively, 𝒜[[X]]) be the ring of polynomials (respectively, power series) with coefficient of degree i in A i for each i ∈ ?. In this paper, we give necessary and sufficient conditions for the rings 𝒜[X] and 𝒜[[X]] to be S ? Noetherian. 相似文献
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5.
A ring R is called clean if every element of R is the sum of an idempotent and a unit. Let M be a R-module. It is obtained in this article that the endomorphism ring End(M) is clean if and only if, whenever A = M′ ⊕ B = A1 ⊕ A2 with M′ ? M, there is a decomposition M′ =M1 ⊕ M2 such that A = M′ ⊕ [A1 ∩ (M1 ⊕ B)] ⊕ [A2 ∩ (M2 ⊕ B)]. Then unit-regular endomorphism rings are also described by direct decompositions. 相似文献
6.
We show that if A is a representation-finite selfinjective Artin algebra, then every P ? ? K b(𝒫 A ) with Hom K(Mod?A)(P ?,P ?[i]) = 0 for i ≠ 0 and add(P ?) = add(νP ?) is a direct summand of a tilting complex, and that if A, B are derived equivalent representation-finite selfinjective Artin algebras, then there exists a sequence of selfinjective Artin algebras A = B 0, B 1,…, B m = B such that, for any 0 ≤ i < m, B i+1 is the endomorphism algebra of a tilting complex for B i of length ≤ 1. 相似文献
7.
Let G be a finite group. A subgroup K of a group G is called an ?-subgroup of G if N G (K) ∩ K x ≦ K for all x ? G. The set of all ?-subgroups of G will be denoted by ?(G). Let P be a nontrivial p-group. A chain of subgroups 1 = P 0 ? P 1 ? ··· ? P n = P is called a maximal chain of P provided that |P i : P i?1| = p, i = 1, 2, ···, n. A nontrivial p-subgroup P of G is called weakly supersolvably embedded in G if P has a maximal chain 1 = P 0 ? P 1 ? ··· ? P i ? ··· ? P n = P such that P i ? ?(G) for i = 1, 2, ···, n. Using the concept of weakly supersolvably embedded, we obtain new characterizations of p-nilpotent and supersolvable finite groups. 相似文献
8.
Let R be a semiprime ring with symmetric Martindale quotient ring Q, n ≥ 2 and let f(X) = X n h(X), where h(X) is a polynomial over the ring of integers with h(0) = ±1. Then there is a ring decomposition Q = Q 1 ⊕ Q 2 ⊕ Q 3 such that Q 1 is a ring satisfying S 2n?2, the standard identity of degree 2n ? 2, Q 2 ? M n (E) for some commutative regular self-injective ring E such that, for some fixed q > 1, x q = x for all x ∈ E, and Q 3 is a both faithful S 2n?2-free and faithful f-free ring. Applying the theorem, we characterize m-power commuting maps, which are defined by linear generalized differential polynomials, on a semiprime ring. 相似文献
9.
André Adler 《随机分析与应用》2013,31(2):339-358
Abstract Consider independent and identically distributed random variables {X nk , 1 ≤ k ≤ m, n ≥ 1} from the Pareto distribution. We randomly select a pair of order statistics from each row, X n(i) and X n(j), where 1 ≤ i < j ≤ m. Then we test to see whether or not Strong and Weak Laws of Large Numbers with nonzero limits for weighted sums of the random variables X n(j)/X n(i) exist where we place a prior distribution on the selection of each of these possible pairs of order statistics. 相似文献
10.
Huanyin Chen 《代数通讯》2013,41(5):1661-1673
A regular ring R is separative provided that for all finitely generated projective right R-modules A and B, A⊕ A? A⊕ B? A⊕ B implies that A? B. We prove, in this article, that a regular ring R in which 2 is invertible is separative if and only if each a ∈ R satisfying R(1 ? a 2)R = Rr(a) = ?(a)R and i(End R (aR)) = ∞ is unit-regular if and only if each a ∈ R satisfying R(1 ? a 2)R ∩ RaR = Rr(a) ∩ ?(a)R ∩ RaR and i(End R (aR)) = ∞ is unit-regular. Further equivalent characterizations of such regular rings are also obtained. 相似文献
11.
For a quiver Q, a k-algebra A, and an additive full subcategory 𝒳 of A-mod, the monomorphism category Mon(Q, 𝒳) is introduced. The main result says that if T is an A-module such that there is an exact sequence 0 → T m → … → T 0 → D(A A ) → 0 with each T i ∈ add(T), then Mon(Q, ⊥ T) =⊥(kQ ? k T); and if T is cotilting, then kQ ? k T is a unique cotilting Λ-module, up to multiplicities of indecomposable direct summands, such that Mon(Q, ⊥ T) =⊥(kQ ? k T). As applications, the category of the Gorenstein-projective (kQ ? k A)-modules is characterized as Mon(Q, 𝒢𝒫(A)) if A is Gorenstein; the contravariantly finiteness of Mon(Q, 𝒳) can be described; and a sufficient and necessary condition for Mon(Q, A) being of finite type is given. 相似文献
12.
《随机分析与应用》2013,31(4):865-894
Abstract It may happen that there is not a finite maximum order bound for numerical approximations of stochastic processes X = (X t : 0 ≤ t ≤ T) satisfying Stratonovich stochastic differential equations (SDEs) with some commutative structure along an appropriate functional V(t, X t ). This statement can be proven with respect to the concept of mean square convergence under the assumption of “infinite smoothness” of drift a(t, x) and diffusion coefficients b j (t, x) and with finite initial second moments. As a result, we obtain an infinite series expansion of the conditional expectation 𝔼[V(t, X t )|? t N ] on any fixed finite time interval [0, T], provided that the information is collected by discretized σ‐field ? T N = σ{W t 0 , W t 1 , …, W t N?1 , W T } at N + 1 given time instants t i ∈ [0, T] with t 0 ≤ t 1 ≤ ··· ≤ t N?1 ≤ t N = T. 相似文献
13.
Mariam Imtiaz 《代数通讯》2013,41(8):3095-3112
Abstract Let R = K[y 1,…,y t ] be an affine domain over a field K and I be a nonzero proper ideal of R. In Sec. 1 of this note, we characterize when (K + I, R) is a Mori pair. In Sec. 2 of this note, we prove the following theorem: Let A ? B be domains such that C/Q is Mori for each subring C of B containing A and for any prime ideal Q of C. Then dim A ? 1 ≤ dim B ≤ dim A + 1 and if dim A > 1 or dim B > 1 then dim A = dim B. 相似文献
14.
Ellen Kirkman 《代数通讯》2013,41(10):3785-3799
It is shown that the global dimension of any n-ary down-up algebra A n = A(n,α, β,γ) is less than or equal to n + 2, and when γ i = 0 for all i (A n is graded by total degree in the generators), then the global dimension of A n is n + 2. Furthermore, a sufficient condition for A n to be prime is given; when γ i = 0 for all i this condition is also necessary. An example is given to show that the condition is not always necessary. 相似文献
15.
A finite group G is said to be a B(n, k) group if for any n-element subset {a 1,…, a n } of G, |{a i a j |1 ≤ i, j ≤ n}| ≤k. In this article, we give characterizations of the B(5, 19) 2-groups, and the B(6, k) 2-groups for 21 ≤ k ≤ 28. 相似文献
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17.
Consider an irreducible polynomial of the form f(X) = X p ? aX ? b ∈ 𝔽[X] and α a root of f(X), where 𝔽 is a field of characteristic p. In 1975, F.J. Sullivan stated a lemma that provides the trace, taken with respect to the extension 𝔽(α)/𝔽, of elements of the form α n , where 0 ≤ n ≤ p 2 ? 1. We present a generalization of Sullivan's Lemma and provide another proof of the original lemma. We explain how computing Tr(α n ) for n < p r can be reduced to computing the traces Tr(α m ) for all m ≤ r(p ? 1). 相似文献
18.
We show that if R is an infinite ring such that XY ∩ YX ≠ ? for all infinite subsets X and Y, then R is commutative. We also prove that in an infinite ring R, an element a ∈ R is central if and only if aX ∩ Xa ≠ ? for all infinite subsets X. 相似文献
19.
Hongbo Zhang 《代数通讯》2013,41(4):1420-1427
An element of a ring R is called “strongly clean” if it is the sum of an idempotent and a unit that commute, and R is called “strongly clean” if every element of R is strongly clean. A module M is called “strongly clean” if its endomorphism ring End(M) is a strongly clean ring. In this article, strongly clean modules are characterized by direct sum decompositions, that is, M is a strongly clean module if and only if whenever M′⊕ B = A 1⊕ A 2 with M′? M, there are decompositions M′ = M 1⊕ M 2, B = B 1⊕ B 2, and A i = C i ⊕ D i (i = 1,2) such that M 1⊕ B 1 = C 1⊕ D 2 = M 1⊕ C 1 and M 2⊕ B 2 = D 1⊕ C 2 = M 2⊕ C 2. 相似文献
20.
《随机分析与应用》2013,31(3):491-509
Abstract Let X 1, X 2… and B 1, B 2… be mutually independent [0, 1]-valued random variables, with EB j = β > 0 for all j. Let Y j = B 1 … sB j?1 X j for j ≥ 1. A complete comparison is made between the optimal stopping value V(Y 1,…,Y n ):=sup{EY τ:τ is a stopping rule for Y 1,…,Y n } and E(max 1≤j≤n Y j ). It is shown that the set of ordered pairs {(x, y):x = V(Y 1,…,Y n ), y = E(max 1≤j≤n Y j ) for some sequence Y 1,…,Y n obtained as described} is precisely the set {(x, y):0 ≤ x ≤ 1, x ≤ y ≤ Ψ n, β(x)}, where Ψ n, β(x) = [(1 ? β)n + 2β]x ? β?(n?2) x 2 if x ≤ β n?1, and Ψ n, β(x) = min j≥1{(1 ? β)jx + β j } otherwise. Sharp difference and ratio prophet inequalities are derived from this result, and an analogous comparison for infinite sequences is obtained. 相似文献