共查询到20条相似文献,搜索用时 46 毫秒
1.
Hirotaka Koga 《代数通讯》2013,41(7):2417-2429
Let R be a commutative noetherian ring and A a noetherian R-algebra. Let P ? ∈ 𝒦b(𝒫 A ) with Hom𝒦(Mod-A)(P ?, P ?[i]) = 0 for i > 0. We will provide a sufficient condition for P ? to be a direct summand of a silting complex. Also, in case Hom𝒦(Mod-A)(P ?, P ?[i]) = 0 for i ≠ 0, we will provide a sufficient condition for P ? to be a direct summand of a tilting complex. 相似文献
2.
Let H = X? R A denote an R-smash product of the two bialgebras X and A. We prove that (X,A) is a pair of matched bialgebras, if the R-smash product H has a braiding structure. When X is an associative algebra and A is a Hopf algebra, we investigate the global dimension and the weak dimension of the smash product H = X? R A and show that lD(H) ≤ rD(A) + lD(X) and wD(H) ≤ wD(A) + wD(X). As an application, we get lD(H 4) = ∞ for Sweedler's four dimensional Hopf algebra H 4. We also study the associativity of smash products and the relations between smash products and factorization for algebras. 相似文献
3.
George Szeto 《代数通讯》2013,41(12):3979-3985
Let B be a Galois algebra over a commutative ring R with Galois group G such that B H is a separable subalgebra of B for each subgroup H of G. Then it is shown that B satisfies the fundamental theorem if and only if B is one of the following three types: (1) B is an indecomposable commutative Galois algebra, (2) B = Re ⊕ R(1 ? e) where e and 1 ? e are minimal central idempotents in B, and (3) B is an indecomposable Galois algebra such that for each separable subalgebra A, V B (A) = ?∑ g∈G(A) J g , and the centers of A and B G(A) are the same where V B (A) is the commutator subring of A in B, J g = {b ∈ B | bx = g(x)b for each x ∈ B} for a g ∈ G, and G(A) = {g ∈ G | g(a) = a for all a ∈ A}. 相似文献
4.
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
5.
Let (T, M) be a complete local domain containing the integers. Let p 1 ? p 2 ? ··· ? p n be a chain of nonmaximal prime ideals of T such that T p n is a regular local ring. We construct a chain of excellent local domains A n ? A n?1 ? ··· ? A 1 such that for each 1 ≤ i ≤ n, the completion of A i is T, the generic formal fiber of A i is local with maximal ideal p i , and if I is a nonzero ideal of A i then A i /I is complete. We then show that if Q is a nonmaximal prime ideal of T and 1 ≤ h = ht T Q, then there is a chain of excellent local domains B 0 ? B 1 ? ··· ? B h ? T such that for every i = 0, 1, 2,…, h we have ht(Q ∩ B i ) = i, the completion of B i is isomorphic to T[[X 1, X 2,…, X i ]] where the X j 's are indeterminants, and the formal fiber of Q ∩ B i is local. 相似文献
6.
Gaywalee Yamskulna 《代数通讯》2013,41(12):4137-4162
We study relationships between vertex Poisson algebras and Courant algebroids. For any ?-graded vertex Poisson algebra A = ? n∈? A (n), we show that A (1) is a Courant A (0)-algebroid. On the other hand, for any Courant 𝒜-algebroid ?, we construct an ?-graded vertex Poisson algebra A = ? n∈? A (n) such that A (0) is 𝒜 and the Courant 𝒜-algebroid A (1) is isomorphic to ? as a Courant 𝒜-algebroid. 相似文献
7.
Gábor P. Nagy 《代数通讯》2013,41(2):549-555
ABSTRACT Let (A, ?) be a structurable algebra. Then the opposite algebra (A op , ?) is structurable, and we show that the triple system B op A(x, y, z):=Vopx,y(z)=x(y¯z)+z(y¯x)?y(x¯z), x, y, z ∈ A, is a Kantor triple system (or generalized Jordan triple system of the second order) satisfying the condition (A). Furthermore, if A=𝔸1?𝔸2 denotes tensor products of composition algebras, (?) is the standard conjugation, and (∧) denotes a certain pseudoconjugation on A, we show that the triple systems B op 𝔸1?𝔸2 ( x , y¯∧, z) are models of compact Kantor triple systems. Moreover these triple systems are simple if (dim𝔸1, dim𝔸2) ≠ (2, 2). In addition, we obtain an explicit formula for the canonical trace form for compact Kantor triple systems defined on tensor products of composition algebras. 相似文献
8.
For an Azumaya algebra A which is free over its centre R, we prove that K-theory of A is isomorphic to K-theory of R up to its rank torsions. We conclude that K i (A, ?/m) = K i (R, ?/m) for any m relatively prime to the rank and i ≥ 0. This covers, for example, K-theory of division algebras, K-theory of Azumaya algebras over semilocal rings, and K-theory of graded central simple algebras indexed by a totally ordered abelian group. 相似文献
9.
Let A be a finite dimensional hereditary algebra over an algebraically closed field and A (m) be the mth replicated algebra of A. We prove that if T is a faithful almost complete tilting A (m)-module with pd A (m) T ≤ m, then T has exactly m + 1 indecomposable nonisomorphic complements with projective dimensions at most m. Moreover, we give an explicit distribution of the complements to T. 相似文献
10.
11.
Let A be a central simple algebra over its center F. Define CK1 A = Coker(K1 F → K1 A). We prove that if A and B are F-central simple algebras of coprime degrees, then CK1(A? F B) = CK1 A × CK1 B. 相似文献
12.
Shuanhong Wang 《代数通讯》2013,41(11):4255-4276
In this article, we provide an alternative approach to the definition of a weak Hopf algebra (WHA). For an associative unital algebra A with a coassociative comultiplication Δ ∈Alg u (A, A ? A), the set of homomorphisms from A to A ? A, which do not preserve the units. If the linear maps Ξ1, Ξ2 ∈ End(A ? A), defined by Ξ1(a ? b) = Δ(a)(1 ? b), Ξ2(a ? b) = (a ? 1)Δ(b), are von Neumann regular elements in the ring End(A ? A) of endomorphisms of A ? A satisfying some appropriate assumptions, we call the A a Hopf-type algebra. We show the existence of a target, a source, a counit, and an antipode of A as in the usual WHA. 相似文献
13.
We studied the solvability of the algebra which satisfies the polynomial identity (x 2)2 = 0. We believe that, if A is a finite dimensional commutative algebra over a field F of characteristic not 2 which satisfies (x 2)2 = 0 for all x ∈ A, then A is solvable. In this article we proved this when dim F A ≤ 7. 相似文献
14.
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
15.
《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
16.
In this paper, we discuss the representation-finite selfinjective artin algebras of classB
n andC
n and obtain the following main results:
For any fieldk, let Λ be a representation-finite selfinjective artin algebras of classB
n orC
n overk.
相似文献
(a) | We give the configuration ofZB n andZC n. |
(b) | We show that Λ is standard. |
(c) | Under the condition ofk being a perfect field, we describe Λ by boundenk-species and show that Λ is a finite covering of the trivial extension of some tilted algebra of typeB n orC n. |
17.
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
18.
ABSTRACT Rank 2-amalgams (P 1, P 2, B), in which P 1/O 2(P 1) ? P 2/O 2(P 2) ? S 5, are analyzed using the amalgam method. It is determined that in the noncommuting case either |O 2(P 1)| = |O 2(P 2)| ≤ 26 or (P 1, P 2, B) has the same shape as an amalgam in Aut(G 2(4)). 相似文献
19.
We consider an inverse boundary value problem for the heat equation ? t u = div (γ? x u) in (0, T) × Ω, u = f on (0, T) × ?Ω, u| t=0 = u 0, in a bounded domain Ω ? ? n , n ≥ 2, where the heat conductivity γ(t, x) is piecewise constant and the surface of discontinuity depends on time: γ(t, x) = k 2 (x ∈ D(t)), γ(t, x) = 1 (x ∈ Ω?D(t)). Fix a direction e* ∈ 𝕊 n?1 arbitrarily. Assuming that ?D(t) is strictly convex for 0 ≤ t ≤ T, we show that k and sup {e*·x; x ∈ D(t)} (0 ≤ t ≤ T), in particular D(t) itself, are determined from the Dirichlet-to-Neumann map : f → ?ν u(t, x)|(0, T)×?Ω. The knowledge of the initial data u 0 is not used in the proof. If we know min0≤t≤T (sup x∈D(t) x·e*), we have the same conclusion from the local Dirichlet-to-Neumann map. Numerical examples of stationary and moving circles inside the unit disk are shown. The results have applications to nondestructive testing. Consider a physical body consisting of homogeneous material with constant heat conductivity except for a moving inclusion with different conductivity. Then the location and shape of the inclusion can be monitored from temperature and heat flux measurements performed at the boundary of the body. Such a situation appears for example in blast furnaces used in ironmaking. 相似文献
20.
Harvey I. Blau 《代数通讯》2017,45(11):4646-4655
We investigate the character values and structures of p-standard table algebras (A,B) with o(B) = pN. If N≤3, then B has a complete normal series. If for every χ∈Irr(B), χ has at most p distinct classes of character values, and if either B has a complete normal series or p = 2, then B is an elementary abelian p-group. 相似文献