共查询到20条相似文献,搜索用时 765 毫秒
1.
Burkhard Külshammer 《代数通讯》2013,41(1):147-168
Abstract Let D be an integral domain. A multiplicative set S of D is an almost splitting set if for each 0 ≠ d ∈ D, there exists an n = n(d) with d n = st where s ∈ S and t is v-coprime to each element of S. An integral domain D is an almost GCD (AGCD) domain if for every x, y ∈ D, there exists a positive integer n = n(x, y) such that x n D ∩ y n D is a principal ideal. We prove that the polynomial ring D[X] is an AGCD domain if and only if D is an AGCD domain and D[X] ? D′[X] is a root extension, where D′ is the integral closure of D. We also show that D + XD S [X] is an AGCD domain if and only if D and D S [X] are AGCD domains and S is an almost splitting set. 相似文献
2.
I. Alrasasi 《代数通讯》2013,41(4):1385-1400
Let D be an integral domain with quotient field K. A Bhargava ring over D is defined to be 𝔹 x (D): = {f ∈ K[X] | ? a ∈ D, f(xX + a) ∈ D[X]}, where x ∈ D. A Bhargava ring over D is a subring of the ring of integer-valued polynomials over D. In this article, we study the prime ideal structure and calculate the Krull and valuative dimension of Bhargava rings over a general domain D. 相似文献
3.
Nicholas J. Werner 《代数通讯》2013,41(12):4717-4726
When D is a commutative integral domain with field of fractions K, the ring Int(D) = {f ∈ K[x] | f(D) ? D} of integer-valued polynomials over D is well-understood. This article considers the construction of integer-valued polynomials over matrix rings with entries in an integral domain. Given an integral domain D with field of fractions K, we define Int(M n (D)): = {f ∈ M n (K)[x] | f(M n (D)) ? M n (D)}. We prove that Int(M n (D)) is a ring and investigate its structure and ideals. We also derive a generating set for Int(M n (?)) and prove that Int(M n (?)) is non-Noetherian. 相似文献
4.
《代数通讯》2013,41(10):5003-5010
Abstract Let R be a prime ring of characteristic different from 2, d a non-zero derivation of R, I a non-zero right ideal of R, a ∈ R, S 4(x 1,…, x 4) the standard polynomial in 4 variables. Suppose that, for any x, y ∈ I, a[d([x, y]), [x, y]] = 0. If S 4(I, I, I, I)I ≠ 0, then aI = ad(I) = 0. 相似文献
5.
Let K be a nonempty closed and convex subset of a real reflexive Banach space X that has weakly sequentially continuous duality mapping J. Let T: K → K be a multivalued non-expansive non-self-mapping satisfying the weakly inwardness condition as well as the condition T(y) = {y} for any y ∈ F(T) and such that for a contraction f: K → K and any t ∈ (0, 1), there exists x t ∈ K satisfying x t ∈ tf(x t ) + (1 ? t)Tx t . Then it is proved that {x t } ? K converges strongly to a fixed point of T, which is also a solution of certain variational inequality. Moreover, the convergence of two explicit methods are also investigated. 相似文献
6.
Ming-Chu Chou 《代数通讯》2013,41(2):898-911
Let R be a prime ring, L a noncentral Lie ideal of R, and a ∈ R. Set [x, y]1 = [x, y] = xy ? yx for x, y ∈ R and inductively [x, y]k = [[x, y]k?1, y] for k > 1. Suppose that δ is a nonzero σ-derivation of R such that a[δ(x), x]k = 0 for all x ∈ L, where σ is an automorphism of R and k is a fixed positive integer. Then a = 0 except when char R = 2 and R ? M2(F), the 2 × 2 matrix ring over a field F. 相似文献
7.
David E. Dobbs 《代数通讯》2013,41(10):3553-3572
Many results on going-down domains and divided domains are generalized to the context of rings with von Neumann regular total quotient rings. A (commutative unital) ring R is called regular divided if each P ∈ Spec(R)?(Max(R) ∩ Min(R)) is comparable with each principal regular ideal of R. Among rings having von Neumann regular total quotient rings, the regular divided rings are the pullbacks K× K/P D where K is von Neumann regular, P ∈ Spec(K) and D is a divided domain. Any regular divided ring (for instance, regular comparable ring) with a von Neumann regular total quotient ring is a weak Baer going-down ring. If R is a weak Baer going-down ring and T is an extension ring with a von Neumann regular total quotient ring such that no regular element of R becomes a zero-divisor in T, then R ? T satisfies going-down. If R is a weak Baer ring and P ∈ Spec(R), then R + PR (P) is a going-down ring if and only if R/P and R P are going-down rings. The weak Baer going-down rings R such that Spec(R)?Min(R) has a unique maximal element are characterized in terms of the existence of suitable regular divided overrings. 相似文献
8.
Ayman Badawi 《代数通讯》2013,41(4):1167-1181
Let R be an integral domain with quotient field K and integral closure R ′. Anderson and Zafrullah called R an “almost valuation domain” if for every nonzero x ∈ K, there is a positive integer n such that either x n ∈ R or x ?n ∈ R. In this article, we introduce a new closely related class of integral domains. We define a prime ideal P of R to be a “pseudo-strongly prime ideal” if, whenever x, y ∈ K and xyP ? P, then there is a positive integer m ≥ 1 such that either x m ∈ R or y m P ? P. If each prime ideal of R is a pseudo-strongly prime ideal, then R is called a “pseudo-almost valuation domain” (PAVD). We show that the class of valuation domains, the class of pseudo-valuation domains, the class of almost valuation domains, and the class of almost pseudo-valuation domains are properly contained in the class of pseudo-almost valuation domains; also we show that the class of pseudo-almost valuation domains is properly contained in the class of quasilocal domains with linearly ordered prime ideals. Among the properties of PAVDs, we show that an integral domain R is a PAVD if and only if for every nonzero x ∈ K, there is a positive integer n ≥ 1 such that either x n ∈ R or ax ?n ∈ R for every nonunit a ∈ R. We show that pseudo-almost valuation domains are precisely the pullbacks of almost valuation domains, we characterize pseudo-almost valuation domains of the form D + M, and we use this characterization to construct PAVDs that are not almost valuation domains. We show that if R is a Noetherian PAVD, then R has Krull dimension at most one and R ′ is a valuation domain; we show that every overring of a PAVD R is a PAVD iff R ′ is a valuation domain and every integral overring of R is a PAVD. 相似文献
9.
Let R be a PID. We construct and classify all coordinates of R[x, y] of the form p 2 y + Q 2(p 1 x + Q 1(y)) with p 1, p 2 ∈ qt(R) and Q 1, Q 2 ∈ qt(R)[y]. From this construction (with R = K[z]) we obtain nontame automorphisms σ of K[x, y, z] (where K is a field of characteristic 0) such that the subgroup generated by σ and the affine automorphisms contains all tame automorphisms. 相似文献
10.
Surjeet Kour 《代数通讯》2013,41(9):4066-4083
If k is a field of characteristic zero, c ∈ k?{0}, s, t ≥ 1, and r ≥ 0 are integers, then it is shown that the k-derivation y r ? x + (y s x t + c)? y of the polynomial algebra k[x, y] is simple. 相似文献
11.
《代数通讯》2013,41(10):4899-4910
Abstract In this paper we show that a regular ring R is a generalized stable ring if and only if for every x ∈ R, there exist a w ∈ K(R) and a group G in R such that wx ∈ G. Also we show that if R is a generalized stable regular ring, then for any A ∈ M n (R), there exist right invertible matrices U 1, U 2 ∈ M n (R) and left invertible matrices V 1, V 2 ∈ M n (R) such that U 1 V 1 AU 2 V 2 = diag(e 1,…, e n ) for some idempotents e 1,…, e n ∈ R. 相似文献
12.
《代数通讯》2013,41(2):1007-1029
Abstract In this paper, we examine the X-inner automorphisms, automorphisms, and isomorphisms of skew polynomial rings of the form K[x][y;δ], where K is a field of characteristic 0 and δ is a derivation of K [x] such that x δ is a polynomial of degree ≥ 1. We 1. determine the group of X-inner automorphisms of K [x][ y;δ], 2. analyze the structure of the group of automorphisms of K [x][ y;δ], and 3. examine the isomorphism classes of skew polynomial rings of the form K [x][ y;δ]. We also provide several examples which indicate the importance of the base field in computing the X-inner automorphisms, automorphisms, and isomorphism classes of K [x][ y;δ]. 相似文献
13.
14.
ABSTRACTLet n≥1 be a fixed integer, R a prime ring with its right Martindale quotient ring Q, C the extended centroid, and L a non-central Lie ideal of R. If F is a generalized skew derivation of R such that (F(x)F(y)?yx)n = 0 for all x,y∈L, then char(R) = 2 and R?M2(C), the ring of 2×2 matrices over C. 相似文献
15.
If k is a field of characteristic zero, c ∈ k?0, and 1 ≤ s ≤ r are integers such that either r ? s + 1 divides s or s divides r ? s + 1, then it is shown that the derivation y r ? x + (xy s + c)? y of the polynomial ring k[x, y] is simple. 相似文献
16.
Cihat Abdioğlu 《代数通讯》2017,45(4):1741-1756
Let R be a noncommutative prime ring with extended centroid C and maximal left ring of quotients Qml(R). The aim of the paper is to study a basic functional identity concerning bi-additive maps on R. Precisely, it is proved that a bi-additive map B:R×R→Qml(R) satisfying [B(x,y),[x,y]] = 0 for all x,y∈R must be of the form (x,y)?λ[x,y]+μ(x,y) for x,y∈R, where λ∈C and μ:R×R→C is a bi-additive map. As applications to the theorem, Jordan σ-biderivations with σ an epimorphism and additive commuting maps on noncommutative Lie ideals of R are characterized. 相似文献
17.
Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, U the right Utumi quotient ring of R, f(x 1,…, x n ) a noncentral multilinear polynomial over K, and G a nonzero generalized derivation of R. Denote f(R) the set of all evaluations of the polynomial f(x 1,…, x n ) in R. If [G(u)u, G(v)v] = 0, for any u, v ∈ f(R), we prove that there exists c ∈ U such that G(x) = cx, for all x ∈ R and one of the following holds: 1. f(x 1,…, x n )2 is central valued on R; 2. R satisfies s 4, the standard identity of degree 4. 相似文献
18.
《代数通讯》2013,41(5):2053-2065
Abstract We consider the group G of C-automorphisms of C(x, y) (resp. C[x, y]) generated by s, t such that t(x) = y, t(y) = x and s(x) = x, s(y) = ? y + u(x) where u ∈ C[x] is of degree k ≥ 2. Using Galois's theory, we show that the invariant field and the invariant algebra of G are equal to C. 相似文献
19.
《代数通讯》2013,41(3):937-951
ABSTRACT Let k be a field, char k ≠ 2, F = k(x), D a biquaternion division algebra over k, and σ an orthogonal involution on D with nontrivial discriminant. We show that there exists a quadratic form ? ∈ I 2(F) such that dim ? = 8, [C(?)] = [D], and ? does not decompose into a direct sum of two forms similar to two-fold Pfister forms. This implies in particular that the field extension F(D)/F is not excellent. Also we prove that if A is a central simple K-algebra of degree 8 with an orthogonal involution σ, then σ is hyperbolic if and only if σ K(A) is hyperbolic. Finally, let σ be a decomposable orthogonal involution on the algebra M 2 m (K). In the case m ≤ 5 we give another proof of the fact that σ is a Pfister involution. If m ≥ 2 n?2 ? 2 and n ≥ 5, we show that q σ ∈ I n (K), where q σ is a quadratic form corresponding to σ. The last statement is founded on a deep result of Orlov et al. (2000) concerning generic splittings of quadratic forms. 相似文献
20.
Let D be an integral domain with quotient field K. We define an element α ∈ K to be pseudo-almost integral over D if there is an infinite increasing sequence {s i } of natural numbers and a nonzero c ∈ D with cα s i ∈ D. We investigate when a pseudo-almost integral element is almost integral or integral. We also determine the sequences {s i } with the property that for any domain D and α ∈ K, whenever cα s i ∈ D for some nonzero c ∈ D, than α is actually almost integral over D. 相似文献