Lie structure in semiprime superalgebrs with superinvolution

Left centralizers on Lie ideals in prime and semiprime gamma rings

Let $U$ be a Lie ideal of a 2-torsion free prime $Γ$-ring $M$ such that $uαu\in U$ for all $u\in U$ and $α\inΓ$. If $T:M\rightarrow M$ is an additive mapping satifying the relation $T(uαu)=T(u)αu$ for all $u\in U$ and $α\inΓ$, then we prove that $T(uαv)=T(u)αv$ for all $u, v\in U$ and $α\inΓ$. Also this result is extended to semiprime $Γ$-rings.

环的 $X$-半素性

The $X$-semiprimeness of Rings

本文引入并研究环的 $X$-半素性，给出 $L$-半素判定准则，刻画素环的相关 Lie 理想，并分析多类环结构的性质。

C*-代数中的素与半素李理想

Prime and semiprime Lie ideals in C*-algebras

本文利用Dixmier理想理论，将C*-代数中的半素与素李理想分别刻画为半素与素双边理想的完全正规化子子空间，并在无特征含单位情形建立自然双射，给出完全非中心的等价条件。

Strongly nondegenerate Lie algebras

Let $A$ be a semiprime 2 and 3-torsion free non-commutative associative algebra. We show that the Lie algebra $\der(A)$ of (associative) derivations of $A$ is strongly non-degenerate, which is a strong form of semiprimeness for Lie algebras, under some additional restrictions on the center of $A$. This result follows from a description of the quadratic annihilator of a general Lie algebra inside appropriate Lie overalgebras. Similar results are obtained for an associative algebra $A$ with involution and the Lie algebra $\sder(A)$ of involution preserving derivations of $A$.

Graded prime ideals over graded Lie algebras

In this work, we extend the definition of the graded prime ideals from those in commutative graded rings to the ideals over graded Lie algebras. We prove some facts about graded prime Lie ideals in arbitrary Lie algebras that are similar to those about graded prime ideals over a commutative or non-commutative ring.In addition, the ideas of graded semiprime Lie ideals and graded total prime Lie ideals will be introduced.

Central extensions of generalized orthosymplectic Lie superalgebras

The key ingredient of this paper is the universal central extension of the generalized orthosymplectic Lie superalgebra $\mathfrak{osp}_{m|2n}(R,{}^-)$ coordinatized by a unital associative superalgebra $(R,{}^-)$ with superinvolution. Such a universal central extension will be constructed via a Steinberg orthosymplectic Lie superalgebra coordinated by $(R,{}^-)$. The research on the universal central extension of $\mathfrak{osp}_{m|2n}(R,{}^-)$ will yield an identification between the second homology group of the generalized orthosymplectic Lie superalgebra $\mathfrak{osp}_{m|2n}(R,{}^-)$ and…

李代数的 Jacobson 纲领

Jacobson program for Lie algebras

本文借鉴环的结构理论，引入李模概念刻画本原李代数，证明表示定理与稠密性定理，并揭示核理想对素和半素李代数的判定作用。

Generalized derivations with central values on lie ideals LIE IDEALS

Let R be a prime ring of H a generalized derivation and L a noncentral lie ideal of R. We show that if l^sH(l)l^t in Z(R) for all lin2 L, where s, t> 0 are fixed integers, then H(x) = bx for some b in C, the extended centroid of R, or R satisfies S4. Moreover, let R be a 2-torsion free semiprime ring, let A = O(R) be an orthogonal completion of R and B = B(C) the Boolean ring of C. Suppose ([x1; x2]sH([x1; x2])[x1; x2]t in Z(R) for all x1; x2 in R, where s, t> 0 are fixed integers. Then there exists idempotent e in B such that H(x) = bx on eA and the ring (1-e)A satisfies S4.

Dhara-Rehman-Raza's identities on left ideals of prime rings

It is known that every nonzero Jordan ideal of $2$-torsion free semiprime rings contains a nonzero ideal. In this paper we show that also any square closed Lie ideal of a $2$-torsion free prime ring contains a nonzero ideal. This can be interpreted by saying that studying identities over one sided ideals is the "optimal" case to study identities. With this fact in mind, we generalize some results of Dhara, Rehman and Raza in [Lie ideals and action of generalized derivations in rings, Miskolc Mathematical Notes, \textbf{16} (2015), 769 -- 779] to the context of nonzero left ideals.