If R is a gr-Jacobson ring(or a gr-prime essential ring,or a gr-essential nilpotent ring),then R is Jacobson ring(or prime essential ring,or essential nilpotent ring).

A commutativity theorem for Jacobson semi-simple rings;

This paper gives and proves two theorems for Jacobson semi-simple rings.

This paper discusses the Nil(R)and Jac(R) of hypercentral extension,which is applied to Azumaya algebra.

This paper proved Vukman s conjecture concerning the image of a linear derivation on a Banach algebra,gave some sufficient conditions that the image of a linear derivation on complex Banach algebra was in the Jacobson radical,and also discussed the simple form of a linear derivation on an annihilator Banach algebra.

Let B be a nuclear C~-algebra with diagonal D in the sense of Kumjian, A a triangular subalgebra of B with diagonal D, then the Jacobson radical of A equals to the topological prime radical of A.

In this paper, we discuss the properties of digraphs for primitive path algebra and (right) Goldie path \{algebra\}; and prove that Brown\|McCoy radical of the generalized path algebra does not coincide with the Jacobson radical in general.

Objective: The aim of this study was to investigate whether cleft palate is associated with the mal_development of the vomer, Jacobson′s organ and para_septal cartilage.