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Let R be a 2-torsion free semiprime *-ring, σ, τ two epimorphisms of R and f, d : R → R two additive mappings. In this paper we prove the following results: (i) d is a Jordan (σ, τ)*-derivation if and only if d is a Jordan triple (σ, τ)*-derivation. (ii) f is a generalized Jordan (σ, τ)*-derivation if and only if f is a generalized Jordan triple (σ, τ)*-derivation. 相似文献
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Tsiu-Kwen Lee 《代数通讯》2013,41(12):5195-5204
Let R be a prime ring which is not commutative, with maximal symmetric ring of quotients Q ms (R), and let τ be an anti-automorphism of R. An additive map δ: R → Q ms (R) is called a Jordan τ-derivation if δ(x 2) = δ(x)x τ + xδ(x) for all x ∈ R. A Jordan τ-derivation of R is called X-inner if it is of the form x → ax τ ? xa for x ∈ R, where a ∈ Q ms (R). It is proved that any Jordan τ-derivation of R is X-inner if either R is not a GPI-ring or R is a PI-ring except when charR = 2 and dim C RC = 4, where C is the extended centroid of R. 相似文献
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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
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By means of partial fraction decomposition, we give simple proofs of Mortenson’s identities first. Then, inspired by them, we derive their q-generalizations and explore further identities of similar type. 相似文献
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《Applied Mathematics Letters》2006,19(10):1122-1128
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Let G be a finite group and σ = {σ i |i∈I} be a partition of the set of all primes P. A set H of subgroups of G is said to be a complete Hall σ-set of G if every non-identity member of H is a Hall σ i -subgroup of G and H contains exactly one Hall σ i -subgroup of G for every σ i ∈ σ(G). A subgroup H is said to be σ-permutable if G possesses a complete Hall σ-set H such that HA x = A x H for all A ∈ H and all x ∈ G. Let H be a subgroup of G. Then we say that: (1) H is σ-embedded in G if there exists a σ-permutable subgroup T of G such that HT = H σG and H ∩ T ≤ H σG , where H σG is the subgroup of H generated by all those subgroups of H which are σ-permutable in G, and H σG is the σ-permutable closure of H, that is, the intersection of all σ-permutable subgroups of G containing H. (2) H is σ-n-embedded in G if there exists a normal subgroup T of G such that HT = H G and H ∩ T ≤ H σG . In this paper, we study the properties of the new embedding subgroups and use them to determine the structure of finite groups. 相似文献
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Siberian Mathematical Journal - Let G be a finite group, and let σ = {σi | i ∈ I} be a partition of the set of all primes ℙ and σ(G) = {σi | σi ∩... 相似文献
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A -frame is a lattice in which countable joins exist and binary meets distribute over countable joins. In this paper, the category MFrm, of metric -frames, is introduced, and it is shown to be equivalent to the category MLFrm
u, of metric Lindelöf frames.Finally, it is shown that the complete metric -frames are exactly the cozero parts of complete metric Lindelöf frames. 相似文献
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The Ramanujan Journal - By studying non-commutative series in an infinite alphabet, we introduce shift-plethystic trees and a class of integer compositions as new combinatorial models for the... 相似文献
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Arc spaces have been introduced in algebraic geometry as a tool to study singularities but they show strong connections with combinatorics as well. Exploiting these relations, we obtain a new approach to the classical Rogers–Ramanujan Identities. The linking object is the Hilbert–Poincaré series of the arc space over a point of the base variety. In the case of the double point, this is precisely the generating series for the integer partitions without equal or consecutive parts. 相似文献