Nonlinear Jordan Derivable Mappings of Generalized Matrix Algebras by Lie Product Square-Zero Elements

The aim of the paper is to give a description of nonlinear Jordan derivable mappings of a certain class of generalized matrix algebras by Lie product square-zero elements. We prove that under certain conditions, a nonlinear Jordan derivable mapping Δ of a generalized matrix algebra by Lie product square-zero elements is a sum of an additive derivation δ and an additive antiderivation f . Moreover, δ and f are uniquely determined.

σ-derivations on generalized matrix algebras

Let 𝒭 be a commutative ring with unity, 𝒜, 𝒝 be 𝒭-algebras, 𝒨 be (𝒜, 𝒝)-bimodule and 𝒩 be (𝒝, 𝒜)-bimodule. The 𝒭-algebra 𝒢 = 𝒢(𝒜, 𝒨, 𝒩, 𝒝) is a generalized matrix algebra defined by the Morita context (𝒜, 𝒝, 𝒨, 𝒩, ξ𝒨𝒩, Ω𝒩𝒨). In this article, we study Jordan σ-derivations on generalized matrix algebras.

The First Hochschild Cohomology of Square Algebras With it's Stability

In this paper, we study on a special case of generalized matrix algebra that we call it square algebra. According to that Hochschild cohomology play a significant role in Geometry for example in orbifolds, we study the first Hochschild cohomology of the square algebra the vanishing of its.

Theory of Adjustments by Least Squares

The concepts of least squares adjustments and the relationships between various types of adjustment are presented in terms of generalized matrix algebra. By developments based on the variance law for independent observations and the linear relationship between independent and correlated observations, variance-covariance matrices and the corresponding weight matrices are developed. The use of generalized matrix algebra permits the derivation of weight matrices from singular, variance-covariance matrices by inversion of the latter matrices. A singular transformation matrix for the elimination of superfluous parameters from observation equations prior to adjustment is presented.