共查询到20条相似文献,搜索用时 15 毫秒
1.
设A为Banach空间X中一自反代数使得在LatA中O ≠0且X_≠X,则A的每一环自同构¢(环反自同构φ)具有形式¢(A)=TAT^-1(φ(A)=TA^*T^-1),其中T:X→X(T:X^*→X)或为一有界线性双射算子或为一有界共轭线性性双射算子。特别地,¢和φ都是连续的。 相似文献
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Zhengxin Chen 《代数通讯》2013,41(2):738-769
Let L be a finite-dimensional complex simple Lie algebra, L ? be the ?-span of a Chevalley basis of L, and L R = R ?? L ? be a Chevalley algebra of type L over a commutative ring R with identity. Let ?(R) be the solvable subalgebra of L R spanned by the basis elements of the maximal toral subalgebra and the root vectors associated with positive roots. In this article, we prove that under some conditions for R, any automorphism of ?(R) is uniquely decomposed as a product of a graph automorphism, a diagonal automorphism and an inner automorphism, and any derivation of ?(R) is uniquely decomposed as a sum of an inner derivation induced by root vectors and a diagonal derivation. Correspondingly, the automorphism group and the derivation algebra of ?(R) are determined. 相似文献
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All automorphisms of the standard Borel subalgebra of the symplectic algebra sp(2m,?R) are determined, provided that R is a commutative ring with identity, 2 is invertible in R. 相似文献
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In this study, by the use of Yuan and Lee’s definition of the fuzzy group based on fuzzy binary operation we give a new kind
of fuzzy ring. The concept of fuzzy subring, fuzzy ideal and fuzzy ring homomorphism are introduced, and we make a theoretical
study their basic properties analogous to those of ordinary rings.
相似文献
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Let L be a finite-dimensional complex simple Lie algebra, L ? be the ?-span of a Chevalley basis of L, and L R = R ?? L ? be a Chevalley algebra of type L over a commutative ring R. Let 𝒩(R) be the nilpotent subalgebra of L R spanned by the root vectors associated with positive roots. A map ? of 𝒩(R) is called commuting if [?(x), x] = 0 for all x ∈ 𝒩(R). In this article, we prove that under some conditions for R, if Φ is not of type A 2, then a derivation (resp., an automorphism) of 𝒩(R) is commuting if and only if it is a central derivation (resp., automorphism), and if Φ is of type A 2, then a derivation (resp., an automorphism) of 𝒩(R) is commuting if and only if it is a sum (resp., a product) of a graded diagonal derivation (resp., automorphism) and a central derivation (resp., automorphism). 相似文献
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V. L. Kurakin 《Mathematical Notes》2006,80(3-4):387-395
Suppose that R is a commutative Artinian chain ring, A is an m × m matrix over R, and S is a discrete valuation ring such that R is a homomorphic image of S. We consider m ideals in the polynomial ring over S that are similarity invariants for matrices over R, i.e., these ideals coincide for similar matrices. It is shown that the new invariants are stronger than the Fitting invariants, and that new invariants solve the similarity problem for 2 × 2 matrices over R. 相似文献
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Ana S?l?gean 《Discrete Applied Mathematics》2006,154(2):413-419
We show that repeated-root cyclic codes over a finite chain ring are in general not principally generated. Repeated-root negacyclic codes are principally generated if the ring is a Galois ring with characteristic a power of 2. For any other finite chain ring they are in general not principally generated. We also prove results on the structure, cardinality and Hamming distance of repeated-root cyclic and negacyclic codes over a finite chain ring. 相似文献
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Fernanda D. de Melo Hernández César A. Hernández Melo Horacio Tapia-Recillas 《代数通讯》2020,48(9):4013-4026
AbstractIn the present work, a procedure for determining idempotents of a commutative ring having a sequence of ideals with certain properties is presented. As an application of this procedure, idempotent elements of various commutative rings are determined. Several examples are included illustrating the main results. 相似文献
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Xing Tao Wang 《代数通讯》2013,41(4):1133-1140
Over a 2-torsionfree commutative ring R with identity, the algebra of all strictly upper triangular n + 1 by n + 1 matrices is denoted by n 1. In this article, we prove that any Jordan automorphism of n 1 can be uniquely decomposed as a product of a graph automorphism, a diagonal automorphism, a central automorphism and an inner automorphism for n ≥ 3. In the cases n = 1, 2, we also give a decomposition for any Jordan automorphism of n 1. 相似文献
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Guifen Zhuang Dragana S. Cvetković-Ilić Yimin Wei 《Linear and Multilinear Algebra》2013,61(8):903-910
In this article, we investigate additive properties on the Drazin inverse of elements in rings. Under the commutative condition of ab?=?ba, we show that a?+?b is Drazin invertible if and only if 1?+?a D b is Drazin invertible. Not only the explicit representations of the Drazin inverse (a?+?b) D in terms of a, a D , b and b D , but also (1?+?a D b) D is given. Further, the same property is inherited by the generalized Drazin invertibility in a Banach algebra and is extended to bounded linear operators. 相似文献
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Paulo Brumatti Philippe Gimenez Aron Simis 《Proceedings of the American Mathematical Society》1996,124(11):3285-3292
We focus on a ``fat' model of an ideal in the class of the canonical ideal of the Segre coordinate ring, looking at its Rees algebra and related arithmetical questions.
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Let 𝒩(∞,R) be the Lie algebra of infinite strictly upper triangular matrices over a commutative ring R. We show that every derivation of 𝒩(∞,R) is a sum of diagonal and inner derivations. 相似文献
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L.J. Ratliff 《Journal of Pure and Applied Algebra》1978,12(2):159-175
A chain condition intermediate to the catenary property and the chain condition for prime ideals (c.c.) is studied. Like the c.c., the condition is inherited from a semi-local domain R by integral extension domains, by local quotient domains, and by factor domains, and a semi-local ring that satisfies the condition is catenary. (Unlike the c.c., none of these statements is true when R is not semi-local.) A number of characterizations of a semi-local domain that satisfies the condition are given in terms of: integral (respectively, algebraic, transcendental) extension domains, Henselizations, completions, Rees rings, associated graded rings and certain discrete valuation over-rings. Then four of the catenary chain conjectures are characterized in terms of this condition. 相似文献
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In this paper, we explore some properties of hulls of cyclic serial codes over a finite chain ring and we provide an algorithm for computing all the possible parameters of the Euclidean hulls of that codes. We also establish the average -dimension of the Euclidean hull, where is the residue field of R, as well as we give some results of its relative growth. 相似文献
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K. N. Ponomarjev 《Acta Appl Math》2005,85(1-3):251-255
We prove that any automorphism of an invariant subalgebra of a reductive Lie algebra over a field of zero characteristic is a standard automorphism.
Mathematics Subject Classifications (2000) 17B20, 17B40. 相似文献
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In this article, the existence of the Drazin (group) inverse of an element a in a ring is analysed when a m k?=?ka n , for some unit k and m, n?∈??. The same problem is studied for the case when a*?=?ka m k ?1 and for the {k, s?+?1}-potent elements. In addition, relationships with other special elements of the ring are also obtained. 相似文献
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Sin-Ei Takahasi Osamu Hatori 《Proceedings of the American Mathematical Society》1999,127(8):2283-2288
We give a structure theorem for a ring homomorphism of a commutative regular Banach algebra into another commutative Banach algebra. In particular, it is shown that:
- (i)
- A ring homomorphism of a commutative -algebra onto another commutative -algebra with connected infinite Gelfand space is either linear or anti-linear.
- (ii)
- A ring automorphism of is either linear or anti-linear.
- (iii)
- , and the disc algebra are neither ring homomorphic images of nor .