-rings of characteristic two that are Boolean.
Jordan- and Lie geometries
In these lecture notes we report on research aiming at understanding the relation beween algebras and geometries, by focusing on the classes of Jordan algebraic and of associative structures and comparing them with Lie structures. The geometric object sought for, called a generalized projective, resp. an associative geometry, can be seen as a combination of the structure of a symmetric space, resp. of a Lie group, with the one of a projective geometry. The text is designed for readers having basic...
Jordan automorphisms, Jordan derivations of generalized triangular matrix algebra.
Jordan automorphisms of triangular algebras. II
We give a sufficient condition under which any Jordan automorphism of a triangular algebra is either an automorphism or an anti-automorphism.
Jordan *-derivation pairs and quadratic functionals on modules over *-rings.
Jordan *-derivation pairs on a complex *-algebra.
Jordan *-derivation pairs on standard operator algebras and related results
Motivated by Problem 2 in [2], Jordan *-derivation pairs and n-Jordan *-mappings are studied. From the results on these mappings, an affirmative answer to Problem 2 in [2] is given when E = F in (1) or when 𝓐 is unital. For the general case, we prove that every Jordan *-derivation pair is automatically real-linear. Furthermore, a characterization of a non-normal prime *-ring under some mild assumptions and a representation theorem for quasi-quadratic functionals are provided.
Jordan ideals and derivations in prime near-rings
In this paper we investigate -prime near-rings with derivations satisfying certain differential identities on Jordan ideals, and we provide examples to show that the assumed restrictions cannot be relaxed.
Jordan left derivations in full and upper triangular matrix rings.
Jordan superderivations and Jordan triple superderivations of superalgebras
We study Jordan (θ,θ)-superderivations and Jordan triple (θ,θ)-superderivations of superalgebras, using the theory of functional identities in superalgebras. As a consequence, we prove that if A = A₀ ⊕ A₁ is a prime superalgebra with deg(A₁) ≥ 9, then Jordan superderivations and Jordan triple superderivations of A are superderivations of A, and generalized Jordan superderivations and generalized Jordan triple superderivations of A are generalized superderivations of A.
Jordan superderivations. II.
Jordan type of a -module.
Jordan types for indecomposable modules of finite group schemes
In this article we study the interplay between algebro-geometric notions related to -points and structural features of the stable Auslander-Reiten quiver of a finite group scheme. We show that -points give rise to a number of new invariants of the AR-quiver on one hand, and exploit combinatorial properties of AR-components to obtain information on -points on the other. Special attention is given to components containing Carlson modules, constantly supported modules, and endo-trivial modules.